Geometric And Topological Aspects Of The Representation Theory Of Finite Groups

Author : Jon F. Carlson,Srikanth B. Iyengar,Julia Pevtsova
Publisher : Springer
Page : 493 pages
File Size : 55,7 Mb
Release : 2018-10-04
Category : Mathematics
ISBN : 9783319940335

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Geometric and Topological Aspects of the Representation Theory of Finite Groups by Jon F. Carlson,Srikanth B. Iyengar,Julia Pevtsova Pdf

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

Author : Anonim
Publisher : Unknown
Page : 493 pages
File Size : 48,9 Mb
Release : 2018
Category : Cohomology operations
ISBN : 3319940341

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Geometric and Topological Aspects of the Representation Theory of Finite Groups by Anonim Pdf

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph. D students transition to independent research.

Author : Shrawan Kumar
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201052

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Kac-Moody Groups, their Flag Varieties and Representation Theory by Shrawan Kumar Pdf

Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.

Author : Mee Seong Im,Bach Nguyen,Arik Wilbert
Publisher : American Mathematical Society
Page : 240 pages
File Size : 47,8 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9781470470340

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Algebraic and Topological Aspects of Representation Theory by Mee Seong Im,Bach Nguyen,Arik Wilbert Pdf

This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20–21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.

Author : Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 46,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401702157

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Cohomology Rings of Finite Groups by Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang Pdf

Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.

Author : T. Tom Dieck
Publisher : Springer
Page : 317 pages
File Size : 51,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385172

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Transformation Groups and Representation Theory by T. Tom Dieck Pdf

Author : V. Lakshmibai,Justin Brown
Publisher : Springer
Page : 172 pages
File Size : 51,7 Mb
Release : 2015-09-25
Category : Mathematics
ISBN : 9781493930821

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The Grassmannian Variety by V. Lakshmibai,Justin Brown Pdf

This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Author : Steven H. Weintraub
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 54,5 Mb
Release : 2003
Category : Finite groups
ISBN : 9780821832226

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Representation Theory of Finite Groups: Algebra and Arithmetic by Steven H. Weintraub Pdf

``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.

Author : Jan Šťovíček,Jan Trlifaj
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 51,9 Mb
Release : 2020-11-13
Category : Education
ISBN : 9781470451318

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Representation Theory and Beyond by Jan Šťovíček,Jan Trlifaj Pdf

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

Author : Jon Carlson,L. Townsley,Luis Valero-Elizondo
Publisher : Unknown
Page : 796 pages
File Size : 49,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401702160

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Cohomology Rings of Finite Groups by Jon Carlson,L. Townsley,Luis Valero-Elizondo Pdf

Author : Henning Krause
Publisher : Cambridge University Press
Page : 517 pages
File Size : 43,9 Mb
Release : 2021-11-18
Category : Mathematics
ISBN : 9781108838894

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Homological Theory of Representations by Henning Krause Pdf

This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.

Author : Martin Burrow
Publisher : Academic Press
Page : 196 pages
File Size : 43,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483258218

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Representation Theory of Finite Groups by Martin Burrow Pdf

Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

Author : Scott Balchin,David Barnes,Magdalena Kędziorek,Markus Szymik
Publisher : Cambridge University Press
Page : 357 pages
File Size : 55,7 Mb
Release : 2021-11-18
Category : Mathematics
ISBN : 9781108931946

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Equivariant Topology and Derived Algebra by Scott Balchin,David Barnes,Magdalena Kędziorek,Markus Szymik Pdf

A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.

Author : Robert R. Bruner,John Rognes
Publisher : American Mathematical Soc.
Page : 690 pages
File Size : 54,8 Mb
Release : 2021-09-30
Category : Education
ISBN : 9781470456740

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The Adams Spectral Sequence for Topological Modular Forms by Robert R. Bruner,John Rognes Pdf

The connective topological modular forms spectrum, tmf, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of tmf and several tmf-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The H∞ ring structure of the sphere and of tmf are used to determine many differentials and relations.

Author : William Mark Goldman,Andy R. Magid
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 54,9 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850824

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Geometry of Group Representations by William Mark Goldman,Andy R. Magid Pdf

The representations of a finitely generated group in a topological group $G$ form a topological space which is an analytic variety if $G$ is a Lie group, or an algebraic variety if $G$ is an algebraic group. The study of this area draws from and contributes to a wide range of mathematical subjects: algebra, analysis, topology, differential geometry, representation theory, and even mathematical physics. In some cases, the space of representations is the object of the study, in others it is a tool in a program of investigation, and, in many cases, it is both. Most of the papers in this volume are based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987.The conference was designed to bring together researchers from the diverse areas of mathematics involving spaces of group representations. In keeping with the spirit of the conference, the papers are directed at nonspecialists, but contain technical developments to bring the subject to the current research frontier. Some of the papers include entirely new results. Readers will gain an understanding of the present state of research in the geometry of group representations and their applications.