Extended Affine Lie Algebras And Their Root Systems

Author : Bruce Normansell Allison,Saeid Azam,Stephen Berman,Arturo Pianzola,Yun Gao
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 51,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805947

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Extended Affine Lie Algebras and Their Root Systems by Bruce Normansell Allison,Saeid Azam,Stephen Berman,Arturo Pianzola,Yun Gao Pdf

This work is about extended affine Lie algebras (EALA's) and their root systems. EALA's were introduced by Hoegh-Krohn and Torresani under the name irreducible quasi-simple Lie algebras. The major objective is to develop enough theory to provide a firm foundation for further study of EALA's. The first chapter of the paper is devoted to establishing some basic structure theory. It includes a proof of the fact that, as conjectured by Kac, the invariant symmetric bilinear form on an EALA can be scaled so that its restriction to the real span of the root system is positive semi-definite. The second chapter studies extended affine root systems (EARS) which are an axiomatized version of the root systems arising from EALA's. The concept of a semilattice is used to give a complete description of EARS. In the final chapter, a number of new examples of extended affine Lie algebras are given. The concluding appendix contains an axiomatic characterization of the nonisotropic roots in an EARS in a more general context than the one used in the rest of the paper. Features: Provides a foundation for the study of an important class of Lie algebras that generalizes the class of affine Kac-Moody Lie algebras Includes material on Lie algebras and on root systems that can be read independently.

Author : Yun Gao
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 48,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821845073

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Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications by Yun Gao Pdf

This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.

Author : Yun Gao, Naihuan Jing, Michael Lau, and Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 53,7 Mb
Release : 2010
Category : Geometry, Affine
ISBN : 9780821858325

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Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications by Yun Gao, Naihuan Jing, Michael Lau, and Kailash C. Misra Pdf

Author : Erhard Neher,Alistair Savage,Weiqiang Wang
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 43,8 Mb
Release : 2011
Category : Nonassociative rings
ISBN : 9780821852378

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Geometric Representation Theory and Extended Affine Lie Algebras by Erhard Neher,Alistair Savage,Weiqiang Wang Pdf

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.

Author : Bruce Normansell Allison,Georgia Benkart,Yun Gao
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 51,8 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821828113

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Lie Algebras Graded by the Root Systems BC$_r$, $r\geq 2$ by Bruce Normansell Allison,Georgia Benkart,Yun Gao Pdf

Introduction The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra, $r\ge 3$ (excluding type $\mathrm{D}_3)$ Models for $\mathrm{BC}_r$-graded Lie algebras, $r\ge 3$ (excluding type $\mathrm{D}_3)$ The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $\mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.

Author : Philippe Gille,Arturo Pianzola
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 40,7 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887745

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Torsors, Reductive Group Schemes and Extended Affine Lie Algebras by Philippe Gille,Arturo Pianzola Pdf

The authors give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that the authors take draws heavily from the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows the authors to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 44,6 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

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Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
Page : 512 pages
File Size : 43,9 Mb
Release : 2016-04-26
Category : Mathematics
ISBN : 9780128046838

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Introduction to Finite and Infinite Dimensional Lie (Super)algebras by Neelacanta Sthanumoorthy Pdf

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 : Ottmar Loos,Erhard Neher
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 44,5 Mb
Release : 2004
Category : Lie superalgebras
ISBN : 9780821835463

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Locally Finite Root Systems by Ottmar Loos,Erhard Neher Pdf

We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: the intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.

Author : Victor G. Kac
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 54,7 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781475713824

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Infinite Dimensional Lie Algebras by Victor G. Kac Pdf

Author : David Mitzman
Publisher : American Mathematical Soc.
Page : 159 pages
File Size : 54,9 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821850435

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Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras by David Mitzman Pdf

This work is a revised version of the author's Ph.D. thesis written under the supervision of J. Lepowsky at Rutgers University in 1983.

Author : Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447148630

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Symmetries, Integrable Systems and Representations by Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy Pdf

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Author : James Lepowsky,John McKay,Michael P. Tuite
Publisher : Cambridge University Press
Page : 415 pages
File Size : 52,7 Mb
Release : 2010-06-03
Category : Mathematics
ISBN : 9780521106641

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Moonshine - The First Quarter Century and Beyond by James Lepowsky,John McKay,Michael P. Tuite Pdf

This volume examines the impact of the 'Monstrous Moonshine' paper on mathematics and theoretical physics.

Author : Roger William Carter
Publisher : Cambridge University Press
Page : 662 pages
File Size : 43,5 Mb
Release : 2005-10-27
Category : Mathematics
ISBN : 0521851386

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Lie Algebras of Finite and Affine Type by Roger William Carter Pdf

This book provides a thorough but relaxed mathematical treatment of Lie algebras.

Author : Lakshmibai V.,V. Balaji,V. B. Mehta,K. R. Nagarajan,K. Pranjape,P. Sankaran,R. Sridharan
Publisher : Springer
Page : 574 pages
File Size : 46,7 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9789386279118

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A Tribute to C.S. Seshadri by Lakshmibai V.,V. Balaji,V. B. Mehta,K. R. Nagarajan,K. Pranjape,P. Sankaran,R. Sridharan Pdf