Loops In Group Theory And Lie Theory

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Loops in Group Theory and Lie Theory

Péter Nagy,Karl Strambach
Loops in Group Theory and Lie Theory Book PDF

Author : Péter Nagy,Karl Strambach
Publisher : Walter de Gruyter
Page : 377 pages
File Size : 44,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110900583

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Loops in Group Theory and Lie Theory by Péter Nagy,Karl Strambach Pdf

In this book the theory of binary systems is considered as a part of group theory and, in particular, within the framework of Lie groups. The novelty is the consequent treatment of topological and differentiable loops as topological and differentiable sections in Lie groups. The interplay of methods and tools from group theory, differential geometry and topology, symmetric spaces, topological geometry, and the theory of foliations is what gives a special flavour to the results presented in this book. It is the first monograph devoted to the study of global loops. So far books on differentiable loops deal with local loops only. This theory can only be used partially for the theory of global loops since non-associative local structures have, in general, no global forms. The text is addressed to researchers in non-associative algebra and foundations of geometry. It should prove enlightening to a broad range of readers, including mathematicians working in group theory, the theory of Lie groups, in differential and topological geometry, and in algebraic groups. The authors have produced a text that is suitable not only for a graduate course, but also for selfstudy in the subjectby interested graduate students. Moreover, the material presented can be used for lectures and seminars in algebra, topological algebra and geometry.

Langlands Correspondence for Loop Groups

Edward Frenkel
Langlands Correspondence for Loop Groups Book PDF

Author : Edward Frenkel
Publisher : Cambridge University Press
Page : 5 pages
File Size : 49,7 Mb
Release : 2007-06-28
Category : Mathematics
ISBN : 9780521854436

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Langlands Correspondence for Loop Groups by Edward Frenkel Pdf

The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.

Ischia Group Theory 2010

Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj
Ischia Group Theory 2010 Book PDF

Author : Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj
Publisher : World Scientific
Page : 416 pages
File Size : 53,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814350389

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Ischia Group Theory 2010 by Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj Pdf

The papers in this volume represent the proceedings of the Conference entitled "Ischia Group Theory 2010," which took place at NH Ischia Thermal SPA Resort, Ischia, Naples, Italy, from April 14 to April 17, 2010. The articles in this volume are contributions by speakers and participants of the Conference. The volume contains a collection of research articles by leading experts in group theory and some accessible surveys of recent research in the area. Together they provide an overview of the diversity of themes and applications that interest group theorists today. Topics covered in this volume include: finite p-groups, character and representation theory, combinatorial group theory, varieties of groups, profinite and pro-p-groups, linear groups, graphs connected with groups, subgroup structure, finiteness conditions, radical rings, conjugacy classes, automorphisms.

Summer School in Group Theory in Banff, 1996

Olga Kharlampovich
Summer School in Group Theory in Banff 1996 Book PDF

Author : Olga Kharlampovich
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 47,9 Mb
Release : 2024-05-05
Category : Mathematics
ISBN : 0821870173

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Summer School in Group Theory in Banff, 1996 by Olga Kharlampovich Pdf

The third annual CRM Summer School took place in Banff (Alberta, Canada) and was aimed toward advanced students and recent PhDs. This volume presents surveys from the group theory part of the theme year and examines different approaches to the topic: a geometric approach, an approach using methods from logic, and an approach with roots in the Bass-Serre theory of groups acting on trees. The work offers a concise introduction to current directions of research in combinatorial group theory. Surveys in the text are by leading researchers in the field who are experienced expositors. The text is suitable for use in a graduate course in geometric and combinatorial group theory.

Lie Groups and Lie Algebras I

V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg
Lie Groups and Lie Algebras I Book PDF

Author : V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 43,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642579998

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Lie Groups and Lie Algebras I by V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg Pdf

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Products of Finite Groups

Adolfo Ballester-Bolinches,Ramon Esteban-Romero,Mohamed Asaad
Products of Finite Groups Book PDF

Author : Adolfo Ballester-Bolinches,Ramon Esteban-Romero,Mohamed Asaad
Publisher : Walter de Gruyter
Page : 347 pages
File Size : 50,7 Mb
Release : 2010-10-19
Category : Mathematics
ISBN : 9783110220612

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Products of Finite Groups by Adolfo Ballester-Bolinches,Ramon Esteban-Romero,Mohamed Asaad Pdf

The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.

Embedding Problems in Symplectic Geometry

Felix Schlenk
Embedding Problems in Symplectic Geometry Book PDF

Author : Felix Schlenk
Publisher : Walter de Gruyter
Page : 261 pages
File Size : 47,8 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110199697

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Embedding Problems in Symplectic Geometry by Felix Schlenk Pdf

Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.

Automatic Sequences

von Friedrich Haeseler
Automatic Sequences Book PDF

Author : von Friedrich Haeseler
Publisher : Walter de Gruyter
Page : 200 pages
File Size : 52,7 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110197969

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Automatic Sequences by von Friedrich Haeseler Pdf

Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words. The text deals with different aspects of automatic sequences, in particular: · a general introduction to automatic sequences · the basic (combinatorial) properties of automatic sequences · the algebraic approach to automatic sequences · geometric objects related to automatic sequences.

Error Calculus for Finance and Physics

Nicolas Bouleau
Error Calculus for Finance and Physics Book PDF

Author : Nicolas Bouleau
Publisher : Walter de Gruyter
Page : 244 pages
File Size : 49,5 Mb
Release : 2003
Category : Business & Economics
ISBN : 9783110180367

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Error Calculus for Finance and Physics by Nicolas Bouleau Pdf

The book deals with propagation of errors on data through mathematical models with applications in finance and physics. It is interesting for scientists and practitioners when studying the sensitivity of their models to small changes in the hypotheses. The book differs from what is usually done in sensitivity analysis because it yields powerful new tools allowing to manage errors in stochastic models as those used in modern finance.

Focus on Group Theory Research

Lawrence M. Ying
Focus on Group Theory Research Book PDF

Author : Lawrence M. Ying
Publisher : Nova Publishers
Page : 176 pages
File Size : 48,9 Mb
Release : 2006
Category : Group theory
ISBN : 1594549672

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Focus on Group Theory Research by Lawrence M. Ying Pdf

A great many of the objects investigated in mathematics turn out to be groups. These include familiar number systems, such as the integers, the rational numbers, the real numbers, and the complex numbers under addition, as well as the non-zero rationals, reals, and complex numbers, under multiplication. Another important example is given by non-singular matrices under multiplication, and more generally, invertible functions under composition. Group theory allows for the properties of these systems and many others to be investigated in a more general setting, and its results are widely applicable. Group theory is also a rich source of theorems in its own right. Groups underlie many other algebraic structures such as fields and vector spaces. They are also important tools for studying symmetry in all its forms; the principle that the symmetries of any object form a group is foundational for much mathematics. For these reasons, group theory is an important area in modern mathematics, and also one with many applications to mathematical physics. This book presents the latest research in the field.

Handbook of Algebra

M. Hazewinkel
Handbook of Algebra Book PDF

Author : M. Hazewinkel
Publisher : Elsevier
Page : 542 pages
File Size : 40,5 Mb
Release : 2006-05-30
Category : Mathematics
ISBN : 0080462499

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Handbook of Algebra by M. Hazewinkel Pdf

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source for information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

Stability Analysis of Impulsive Functional Differential Equations

Ivanka Stamova
Stability Analysis of Impulsive Functional Differential Equations Book PDF

Author : Ivanka Stamova
Publisher : Walter de Gruyter
Page : 241 pages
File Size : 52,5 Mb
Release : 2009-10-16
Category : Mathematics
ISBN : 9783110221824

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Stability Analysis of Impulsive Functional Differential Equations by Ivanka Stamova Pdf

This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.

Analysis, Applications, and Computations

Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas
Analysis Applications and Computations Book PDF

Author : Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas
Publisher : Springer Nature
Page : 696 pages
File Size : 43,9 Mb
Release : 2023-12-01
Category : Mathematics
ISBN : 9783031363757

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Analysis, Applications, and Computations by Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas Pdf

This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Lie Groups and Lie Algebras I

V.V. Gorbatsevich,E.B. Vinberg
Lie Groups and Lie Algebras I Book PDF

Author : V.V. Gorbatsevich,E.B. Vinberg
Publisher : Springer Science & Business Media
Page : 552 pages
File Size : 48,5 Mb
Release : 1996-12-18
Category : Mathematics
ISBN : 354061222X

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Lie Groups and Lie Algebras I by V.V. Gorbatsevich,E.B. Vinberg Pdf

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Non-Associative Algebra and Its Applications

Lev Sabinin,Larissa Sbitneva,Ivan Shestakov
Non Associative Algebra and Its Applications Book PDF

Author : Lev Sabinin,Larissa Sbitneva,Ivan Shestakov
Publisher : CRC Press
Page : 552 pages
File Size : 41,7 Mb
Release : 2006-01-13
Category : Mathematics
ISBN : 1420003453

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Non-Associative Algebra and Its Applications by Lev Sabinin,Larissa Sbitneva,Ivan Shestakov Pdf

With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.