The Book Of Involutions

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The Book of Involutions

Max-Albert Knus
The Book of Involutions Book PDF

Author : Max-Albert Knus
Publisher : American Mathematical Soc.
Page : 624 pages
File Size : 46,9 Mb
Release : 1998-06-30
Category : Mathematics
ISBN : 0821873210

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The Book of Involutions by Max-Albert Knus Pdf

This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings

The Book of Involutions

Max-Albert Knus,Alexander Merkurjev,Markus Rost,Jean-Pierre Tignol
The Book of Involutions Book PDF

Author : Max-Albert Knus,Alexander Merkurjev,Markus Rost,Jean-Pierre Tignol
Publisher : American Mathematical Soc.
Page : 617 pages
File Size : 55,8 Mb
Release : 1998
Category : Formes hermitiennes
ISBN : 9780821809044

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The Book of Involutions by Max-Albert Knus,Alexander Merkurjev,Markus Rost,Jean-Pierre Tignol Pdf

Written for graduate students and research mathematicians, this monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. Involutions are viewed as twisted forms of hermitian quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are discussed, as well as: groups of type F4 or G2 arising from exceptional Jordan or composition algebras, the discriminant algebra of an algebra with unitary involution, and the algebra-theoretic counterpart to linear groups of type D4. Annotation copyrighted by Book News, Inc., Portland, OR.

The Book of Involutions

Anonim
The Book of Involutions Book PDF

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,6 Mb
Release : 1998
Category : Galois theory
ISBN : 1470431904

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The Book of Involutions by Anonim Pdf

This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type F_4 or G_2 arising from exceptional Jordan or composition algebras. Several results and.

Involution

Werner M. Seiler
Involution Book PDF

Author : Werner M. Seiler
Publisher : Springer Science & Business Media
Page : 663 pages
File Size : 43,6 Mb
Release : 2009-10-26
Category : Mathematics
ISBN : 9783642012877

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Involution by Werner M. Seiler Pdf

The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.

Involutions on Manifolds

Santiago Lopez de Medrano
Involutions on Manifolds Book PDF

Author : Santiago Lopez de Medrano
Publisher : Springer Science & Business Media
Page : 114 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642650123

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Involutions on Manifolds by Santiago Lopez de Medrano Pdf

This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space.

Cohomological Invariants in Galois Cohomology

Skip Garibaldi,Alexander Merkurjev,Jean-Pierre Serre
Cohomological Invariants in Galois Cohomology Book PDF

Author : Skip Garibaldi,Alexander Merkurjev,Jean-Pierre Serre
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 54,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832875

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Cohomological Invariants in Galois Cohomology by Skip Garibaldi,Alexander Merkurjev,Jean-Pierre Serre Pdf

This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field. The authors are well-known experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, co-wrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here. The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number th

Quaternion Algebras

John Voight
Quaternion Algebras Book PDF

Author : John Voight
Publisher : Springer Nature
Page : 877 pages
File Size : 45,5 Mb
Release : 2021-06-28
Category : Mathematics
ISBN : 9783030566944

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Quaternion Algebras by John Voight Pdf

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

The Monster Group and Majorana Involutions

Aleksandr Anatolievich Ivanov
The Monster Group and Majorana Involutions Book PDF

Author : Aleksandr Anatolievich Ivanov
Publisher : Cambridge University Press
Page : 267 pages
File Size : 50,9 Mb
Release : 2009-03-19
Category : Mathematics
ISBN : 9780521889940

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The Monster Group and Majorana Involutions by Aleksandr Anatolievich Ivanov Pdf

A rigorous construction and uniqueness proof for the Monster group, detailing its relation to Majorana involutions.

Quadratic and Hermitian Forms over Rings

Max-Albert Knus
Quadratic and Hermitian Forms over Rings Book PDF

Author : Max-Albert Knus
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642754012

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Quadratic and Hermitian Forms over Rings by Max-Albert Knus Pdf

From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.

Architectural Involutions

Mimi Yiu
Architectural Involutions Book PDF

Author : Mimi Yiu
Publisher : Northwestern University Press
Page : 331 pages
File Size : 43,9 Mb
Release : 2015-11-15
Category : Architecture
ISBN : 9780810129863

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Architectural Involutions by Mimi Yiu Pdf

Taking the reader on an inward journey from façades to closets, from physical to psychic space, Architectural Involutions offers an alternative genealogy of theater by revealing how innovations in architectural writing and practice transformed an early modern sense of interiority. As the English house underwent a process of inward folding, replacing a logic of central assembly with one of dissemination, the subject who negotiated this new scenography became a flashpoint of conflict in both domestic and theatrical arenas. The book launches from a matrix of related “platforms”—a term that in early modern usage denoted scaffolds, stages, and draftsmen’s sketches—to situate Alberti, Shakespeare, Jonson, and others within a landscape of spatial and visual change. Engaging theory with archival findings, Mimi Yiu reveals an emergent desire to perform subjectivity, to unfold an interior face to an admiring public.

An Introduction to Symmetric Functions and Their Combinatorics

Eric S. Egge
An Introduction to Symmetric Functions and Their Combinatorics Book PDF

Author : Eric S. Egge
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 51,5 Mb
Release : 2019-11-18
Category : Education
ISBN : 9781470448998

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An Introduction to Symmetric Functions and Their Combinatorics by Eric S. Egge Pdf

This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution ω ω; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results. The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.

Structure of Algebras

Abraham Adrian Albert
Structure of Algebras Book PDF

Author : Abraham Adrian Albert
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 44,5 Mb
Release : 1939-12-31
Category : Mathematics
ISBN : 9780821810248

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Structure of Algebras by Abraham Adrian Albert Pdf

The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI consists of the study of the abelian group of cyclic systems which is applied in Chapter VII to yield the theory of the structure of direct products of cyclic algebras and the consequent properties of norms in cyclic fields. This chapter is closed with the theory of $p$-algebras. In Chapter VIII an exposition is given of the theory of the representations of algebras. The treatment is somewhat novel in that while the recent expositions have used representation theorems to obtain a number of results on algebras, here the theorems on algebras are themselves used in the derivation of results on representations. The presentation has its inspiration in the author's work on the theory of Riemann matrices and is concluded by the introduction to the generalization (by H. Weyl and the author) of that theory. The theory of involutorial simple algebras is derived in Chapter X both for algebras over general fields and over the rational field. The results are also applied in the determination of the structure of the multiplication algebras of all generalized Riemann matrices, a result which is seen in Chapter XI to imply a complete solution of the principal problem on Riemann matrices.

Quadratic Forms, Linear Algebraic Groups, and Cohomology

Skip Garibaldi,R. Sujatha,Venapally Suresh
Quadratic Forms Linear Algebraic Groups and Cohomology Book PDF

Author : Skip Garibaldi,R. Sujatha,Venapally Suresh
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 45,5 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9781441962119

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Quadratic Forms, Linear Algebraic Groups, and Cohomology by Skip Garibaldi,R. Sujatha,Venapally Suresh Pdf

Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.

A3 & His Algebra

Nancy E. Albert,Nancy Albert-Goldberg
A3 His Algebra Book PDF

Author : Nancy E. Albert,Nancy Albert-Goldberg
Publisher : iUniverse
Page : 368 pages
File Size : 46,6 Mb
Release : 2005
Category : Biography & Autobiography
ISBN : 9780595328178

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A3 & His Algebra by Nancy E. Albert,Nancy Albert-Goldberg Pdf

A3 & HIS ALGEBRA is the true story of a struggling young boy from Chicago's west side who grew to become a force in American mathematics. For nearly 50 years, A. A. Albert thrived at the University of Chicago, one of the world's top centers for algebra. His "pure research" in algebra found its way into modern computers, rocket guidance systems, cryptology, and quantum mechanics, the basic theory behind atomic energy calculations. This first-hand account of the life of a world-renowned American mathematician is written by Albert's daughter. Her memoir, which favors a general audience, offers a personal and revealing look at the multidimensional life of an academic who had a lasting impact on his profession. SOME QUOTATIONS FROM PROFESSOR ALBERT: "There are really few bad students of mathematics. There are, instead, many bad teachers and bad curricula..." "The difficulty of learning mathematics is increased by the fact that in so many high schools this very difficult subject is considered to be teachable by those whose major subject is language, botany, or even physical education." "It is still true that in a majority of American universities the way to find the Department of Mathematics is to ask for the location of the oldest and most decrepit building on campus." "The production of a single scientist of first magnitude will have a greater impact on our civilization than the production of fifty mediocre Ph.D.'s." "Freedom is having the time to do research...Even in mathematics there are 'fashions'. This doesn't mean that the researcher is controlled by them. Many go their own way, ignoring the fashionable. That's part of the strength of a great university."

Quadratic and Hermitian Forms

W. Scharlau
Quadratic and Hermitian Forms Book PDF

Author : W. Scharlau
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642699719

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Quadratic and Hermitian Forms by W. Scharlau Pdf

For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms. On the basis of their work, Minkowski, Siegel, Hasse, Eichler and many others crea ted the impressive "arithmetic" theory of quadratic forms, which has been the object of the well-known books by Bachmann (1898/1923), Eichler (1952), and O'Meara (1963). Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both - the number theory of quadratic forms and the ideas of modern algebra - Witt opened, in 1937, a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object. This object - the Witt ring - then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems.