Extensions Of Representations Of Lie Algebras
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Author | : Gerhard Paul Hochschild |
Publisher | : |
Total Pages | : 62 |
Release | : 1957 |
Genre | : Lie algebras |
ISBN | : |
Download Extensions of Representations of Lie Groups and Lie Algebras Book in PDF, Epub and Kindle
Author | : John Gerard Ryan |
Publisher | : |
Total Pages | : 104 |
Release | : 1984 |
Genre | : |
ISBN | : |
Download Extensions of Representations of Lie Algebras Book in PDF, Epub and Kindle
Author | : George D. Mostow |
Publisher | : |
Total Pages | : 56 |
Release | : 1957 |
Genre | : Lie algebras |
ISBN | : |
Download Extensions of Representations of Lie Groups II. Book in PDF, Epub and Kindle
Author | : James E. Humphreys |
Publisher | : American Mathematical Soc. |
Total Pages | : 289 |
Release | : 2021-07-14 |
Genre | : Education |
ISBN | : 1470463261 |
Download Representations of Semisimple Lie Algebras in the BGG Category O Book in PDF, Epub and Kindle
This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g g over C C. The setting is the module category O O introduced by Bernstein–Gelfand–Gelfand, which includes all highest weight modules for g g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g g. Basic techniques in category O O such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D D-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O O, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.
Author | : Nathan Jacobson |
Publisher | : Courier Corporation |
Total Pages | : 348 |
Release | : 2013-09-16 |
Genre | : Mathematics |
ISBN | : 0486136795 |
Download Lie Algebras Book in PDF, Epub and Kindle
DIVDefinitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, etc. Index. /div
Author | : Gerhard Paul Hochschild |
Publisher | : |
Total Pages | : 60 |
Release | : 1957 |
Genre | : Lie algebras |
ISBN | : |
Download Extensions of Representations of Lie Groups and Lie Algebras Book in PDF, Epub and Kindle
Author | : Alexander A. Kirillov |
Publisher | : Cambridge University Press |
Total Pages | : 237 |
Release | : 2008-07-31 |
Genre | : Mathematics |
ISBN | : 0521889693 |
Download An Introduction to Lie Groups and Lie Algebras Book in PDF, Epub and Kindle
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author | : Neelacanta Sthanumoorthy |
Publisher | : Academic Press |
Total Pages | : 514 |
Release | : 2016-04-26 |
Genre | : Mathematics |
ISBN | : 012804683X |
Download Introduction to Finite and Infinite Dimensional Lie (Super)algebras Book in PDF, Epub and Kindle
Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras
Author | : Robert N. Cahn |
Publisher | : Courier Corporation |
Total Pages | : 180 |
Release | : 2014-06-10 |
Genre | : Mathematics |
ISBN | : 0486150313 |
Download Semi-Simple Lie Algebras and Their Representations Book in PDF, Epub and Kindle
Designed to acquaint students of particle physiME already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has provided a new preface for this edition. Subjects include the killing form, the structure of simple Lie algebras and their representations, simple roots and the Cartan matrix, the classical Lie algebras, and the exceptional Lie algebras. Additional topiME include Casimir operators and Freudenthal's formula, the Weyl group, Weyl's dimension formula, reducing product representations, subalgebras, and branching rules. 1984 edition.
Author | : Erhard Neher |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 082185237X |
Download Geometric Representation Theory and Extended Affine Lie Algebras Book in PDF, Epub and Kindle
Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.