Author: William Joseph Haboush Brian ParshallPublisher: American Mathematical Soc.
ISBN: 9780821868287
Category : Linear algebraic groups
Languages : en
Pages : 442
Book Description
Algebraic groups and their generalizations: Quantum and infinite-dimensional methods
Author: William Joseph Haboush Brian ParshallPublisher: American Mathematical Soc.
ISBN: 9780821868287
Category : Linear algebraic groups
Languages : en
Pages : 442
Book Description
Algebraic groups and their generalizations
Author: William Joseph Haboush (mathématicien).)Publisher:
ISBN: 9780821815410
Category : Linear algebraic groups
Languages : en
Pages : 415
Book Description
Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional Methods
Author: William Joseph HaboushPublisher: American Mathematical Soc.
ISBN: 0821815415
Category : Mathematics
Languages : en
Pages : 429
Book Description
Proceedings of a research institute held at Pennsylvania State University, July 1991, focusing on quantum and infinite-dimensional methods of algebraic groups. Topics include perverse sheaves, finite Chevalley groups, the general theory of algebraic groups, representations, invariant theory, general
Algebraic Groups and Their Generalizations
Author: Publisher:
ISBN:
Category : Linear algebraic groups
Languages : en
Pages : 383
Book Description
Algebraic Groups and Their Generalizations: Classical Methods
Author: William Joseph HaboushPublisher: American Mathematical Soc.
ISBN: 0821815407
Category : Mathematics
Languages : en
Pages : 397
Book Description
Infinite Dimensional Groups and Algebras in Quantum Physics
Author: Johnny T. OttesenPublisher: Springer Science & Business Media
ISBN: 3540491414
Category : Science
Languages : en
Pages : 223
Book Description
The idea of writing this book appeared when I was working on some problems related to representations of physically relevant infinite - mensional groups of operators on physically relevant Hilbert spaces. The considerations were local, reducing the subject to dealing with representations of infinite-dimensional Lie algebras associated with the associated groups. There is a large number of specialized articles and books on parts of this subject, but to our suprise only a few represent the point of view given in this book. Moreover, none of the written material was self-contained. At present, the subject has not reached its final form and active research is still being undertaken. I present this subject of growing importance in a unified manner and by a fairly simple approach. I present a route by which students can absorb and understand the subject, only assuming that the reader is familliar with functional analysis, especially bounded and unbounded operators on Hilbert spaces. Moreover, I assume a little basic knowledge of algebras , Lie algebras, Lie groups, and manifolds- at least the definitions. The contents are presented in detail in the introduction in Chap. The manuscript of this book has been succesfully used by some advanced graduate students at Aarhus University, Denmark, in their "A-exame'. I thank them for comments.
Infinite-Dimensional Representations of 2-Groups
Author: John C. BaezPublisher: American Mathematical Soc.
ISBN: 0821872842
Category : Mathematics
Languages : en
Pages : 133
Book Description
Just as groups can have representations on vector spaces, 2-groups have representations on 2-vector spaces, but Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. Therefore, Crane, Sheppeard, and Yetter introduced certain infinite-dimensional 2-vector spaces, called measurable categories, to study infinite-dimensional representations of certain Lie 2-groups, and German and North American mathematicians continue that work here. After introductory matters, they cover representations of 2-groups, and measurable categories, representations on measurable categories. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Finite Dimensional Algebras and Quantum Groups
Author: Bangming DengPublisher: American Mathematical Soc.
ISBN: 0821841866
Category : Mathematics
Languages : en
Pages : 790
Book Description
"The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.
Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
Author: Thomas KerlerPublisher: Springer
ISBN: 3540446257
Category : Mathematics
Languages : en
Pages : 381
Book Description
This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.
Recent Developments in Quantum Affine Algebras and Related Topics
Author: Naihuan JingPublisher: American Mathematical Soc.
ISBN: 0821811991
Category : Mathematics
Languages : en
Pages : 482
Book Description
This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.