Lectures On Duflo Isomorphisms In Lie Algebra And Complex Geometry

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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry

Damien Calaque,Carlo Antonio Rossi
Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry Book PDF

Author : Damien Calaque,Carlo Antonio Rossi
Publisher : European Mathematical Society
Page : 120 pages
File Size : 44,6 Mb
Release : 2011
Category : Cohomology operations
ISBN : 3037190965

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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry by Damien Calaque,Carlo Antonio Rossi Pdf

The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for $Q$-manifolds. All notions mentioned above are introduced and explained in this book. The only prerequisites are basic linear algebra and differential geometry. In addition to standard notions such as Lie (super) algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in detail. This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.

Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry

DAMIEN CALAQUE; CARLO A. ROSSI.,Damien Calaque
Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry Book PDF

Author : DAMIEN CALAQUE; CARLO A. ROSSI.,Damien Calaque
Publisher : Unknown
Page : 106 pages
File Size : 45,5 Mb
Release : 2024-06-27
Category : Isomorphisms (Mathematics)
ISBN : 3037195967

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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry by DAMIEN CALAQUE; CARLO A. ROSSI.,Damien Calaque Pdf

Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Later on, Duflo's result was refound by Kontsevich in the framework of deformation quantization, who also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. The present book, which arose from a series of lectures by the first author at ETH, derives these two isomorphisms from a Duflo-type result for Q-manifolds. All notions mentioned above are introduced and explained in the book, the only prerequisites being basic linear algebra and differential geometry. In addition to standard notions such as Lie (super)algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in details. The book is well-suited for graduate students in mathematics and mathematical physics as well as for researchers working in Lie theory, algebraic geometry and deformation theory.

A Course on Elation Quadrangles

Koen Thas
A Course on Elation Quadrangles Book PDF

Author : Koen Thas
Publisher : European Mathematical Society
Page : 136 pages
File Size : 51,8 Mb
Release : 2012
Category : Abelian p-groups
ISBN : 3037191104

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A Course on Elation Quadrangles by Koen Thas Pdf

The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring, for instance, Knarr's question from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor's prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as $p$-modular cohomology, Heisenberg groups, and existence problems for certain translation nets, are briefly touched. This book starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. This course contains dozens of exercises at various levels, from very easy to rather difficult, and will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. More accomplished mathematicians will find the final chapters especially challenging.

Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration

Hans Triebel
Faber Systems and Their Use in Sampling Discrepancy Numerical Integration Book PDF

Author : Hans Triebel
Publisher : European Mathematical Society
Page : 120 pages
File Size : 43,7 Mb
Release : 2012
Category : Function spaces
ISBN : 3037191074

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Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration by Hans Triebel Pdf

This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book, ``Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration'' (EMS, 2010), from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals.

Mathematical Foundations of Supersymmetry

Claudio Carmeli,Lauren Caston,Rita Fioresi
Mathematical Foundations of Supersymmetry Book PDF

Author : Claudio Carmeli,Lauren Caston,Rita Fioresi
Publisher : European Mathematical Society
Page : 308 pages
File Size : 46,9 Mb
Release : 2011
Category : Lie algebras
ISBN : 3037190973

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Mathematical Foundations of Supersymmetry by Claudio Carmeli,Lauren Caston,Rita Fioresi Pdf

Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, as well as detailed proofs and many clarifying examples. This book is aimed ideally at second-year graduate students. After the first three introductory chapters, the text is divided into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices. The first introduces Lie superalgebras and representations of classical Lie superalgebras, the second collects some relevant facts on categories, sheafification of functors and commutative algebra, and the third explains the notion of Frechet space in the super context.

Lie Algebras, Geometry, and Toda-Type Systems

Alexander Vitalievich Razumov,Mikhail V. Saveliev
Lie Algebras Geometry and Toda Type Systems Book PDF

Author : Alexander Vitalievich Razumov,Mikhail V. Saveliev
Publisher : Cambridge University Press
Page : 271 pages
File Size : 55,7 Mb
Release : 1997-05-15
Category : Mathematics
ISBN : 9780521479233

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Lie Algebras, Geometry, and Toda-Type Systems by Alexander Vitalievich Razumov,Mikhail V. Saveliev Pdf

The book describes integrable Toda type systems and their Lie algebra and differential geometry background.

Lectures on Real Semisimple Lie Algebras and Their Representations

A. L. Onishchik
Lectures on Real Semisimple Lie Algebras and Their Representations Book PDF

Author : A. L. Onishchik
Publisher : European Mathematical Society
Page : 100 pages
File Size : 55,5 Mb
Release : 2004
Category : Mathematics
ISBN : 3037190027

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Lectures on Real Semisimple Lie Algebras and Their Representations by A. L. Onishchik Pdf

The book begins with a simplified (and somewhat extended and corrected) exposition of the main results of F. Karpelevich's 1955 paper and relates them to the theory of Cartan-Iwahori. It concludes with some tables, where an involution of the Dynkin diagram that allows for finding self-conjugate representations is described and explicit formulas for the index are given. In a short addendum, written by J. V. Silhan, this involution is interpreted in terms of the Satake diagram.

Lectures On Algebraic Topology

Haynes R Miller
Lectures On Algebraic Topology Book PDF

Author : Haynes R Miller
Publisher : World Scientific
Page : 405 pages
File Size : 42,8 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9789811231261

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Lectures On Algebraic Topology by Haynes R Miller Pdf

Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.

Lectures on Exceptional Lie Groups

J. F. Adams
Lectures on Exceptional Lie Groups Book PDF

Author : J. F. Adams
Publisher : University of Chicago Press
Page : 136 pages
File Size : 47,9 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 0226005275

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Lectures on Exceptional Lie Groups by J. F. Adams Pdf

J. Frank Adams was internationally known and respected as one of the great algebraic topologists. Adams had long been fascinated with exceptional Lie groups, about which he published several papers, and he gave a series of lectures on the topic. The author's detailed lecture notes have enabled volume editors Zafer Mahmud and Mamoru Mimura to preserve the substance and character of Adams's work. Because Lie groups form a staple of most mathematics graduate students' diets, this work on exceptional Lie groups should appeal to many of them, as well as to researchers of algebraic geometry and topology. J. Frank Adams was Lowndean professor of astronomy and geometry at the University of Cambridge. The University of Chicago Press published his Lectures on Lie Groups and has reprinted his Stable Homotopy and Generalized Homology. Chicago Lectures in Mathematics Series

An Introduction to Lie Groups and Lie Algebras

Alexander A. Kirillov
An Introduction to Lie Groups and Lie Algebras Book PDF

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 44,5 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Algebra, Arithmetic, and Geometry

Yuri Tschinkel,Yuri Zarhin
Algebra Arithmetic and Geometry Book PDF

Author : Yuri Tschinkel,Yuri Zarhin
Publisher : Springer Science & Business Media
Page : 723 pages
File Size : 47,8 Mb
Release : 2010-08-05
Category : Mathematics
ISBN : 9780817647452

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Algebra, Arithmetic, and Geometry by Yuri Tschinkel,Yuri Zarhin Pdf

EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

Dirac Operators in Representation Theory

Jing-Song Huang,Pavle Pandzic
Dirac Operators in Representation Theory Book PDF

Author : Jing-Song Huang,Pavle Pandzic
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 40,6 Mb
Release : 2007-05-27
Category : Mathematics
ISBN : 9780817644932

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Dirac Operators in Representation Theory by Jing-Song Huang,Pavle Pandzic Pdf

This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.

Tensor Categories

Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Tensor Categories Book PDF

Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 44,8 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410

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Tensor Categories by Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik Pdf

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Déformation, quantification, théorie de Lie

Alberto S. Cattaneo,Alberto Cattaneo
D formation quantification th orie de Lie Book PDF

Author : Alberto S. Cattaneo,Alberto Cattaneo
Publisher : Societe Mathematique de France
Page : 210 pages
File Size : 44,9 Mb
Release : 2005
Category : Business & Economics
ISBN : UOM:39015068671067

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Déformation, quantification, théorie de Lie by Alberto S. Cattaneo,Alberto Cattaneo Pdf

In 1997, M. Kontsevich proved that every Poisson manifold admits a formal quantization, canonical up to equivalence. In doing so he solved a longstanding problem in mathematical physics. Through his proof and his interpretation of a later proof given by Tamarkin, he also opened up new research avenues in Lie theory, quantum group theory, deformation theory and the study of operads ... and uncovered fascinating links of these topics with number theory, knot theory and the theory of motives. Without doubt, his work on deformation quantization will continue to influence these fields for many years to come. In the three parts of this volume, we will 1) present the main results of Kontsevich's 1997 preprint and sketch his interpretation of Tamarkin's approach, 2) show the relevance of Kontsevich's theorem for Lie theory and 3) explain the idea from topological string theory which inspired Kontsevich's proof. An appendix is devoted to the geometry of configuration spaces.

Hamiltonian Reduction by Stages

Jerrold E. Marsden,Gerard Misiolek,Juan-Pablo Ortega,Matthew Perlmutter,Tudor S. Ratiu
Hamiltonian Reduction by Stages Book PDF

Author : Jerrold E. Marsden,Gerard Misiolek,Juan-Pablo Ortega,Matthew Perlmutter,Tudor S. Ratiu
Publisher : Springer
Page : 524 pages
File Size : 49,5 Mb
Release : 2007-06-05
Category : Mathematics
ISBN : 9783540724704

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Hamiltonian Reduction by Stages by Jerrold E. Marsden,Gerard Misiolek,Juan-Pablo Ortega,Matthew Perlmutter,Tudor S. Ratiu Pdf

This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.