Rational methods in Lie algebras

Author: George B. Seligman

Publisher: Marcel Dekker Inc

ISBN: N.A

Category: Mathematics

Page: 346

View: 8171

Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications

Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, March 2-7, 2008, Banff International Research Station, Banff, Canada

Author: Yun Gao

Publisher: American Mathematical Soc.

ISBN: 0821845071

Category: Mathematics

Page: 302

View: 8628

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.

Lie Algebras and Related Topics

Proceedings of a Summer Seminar Held June 26-July 6, 1984

Author: Daniel J. Britten,Frank W. Lemire,R. V. Moody,Natural Sciences and Engineering Research Council Canada

Publisher: American Mathematical Soc.

ISBN: 9780821860090

Category: Mathematics

Page: 382

View: 3940

Focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. This work features papers including a survey article on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras, a course on Kac-Moody Lie algebras and a course on formal groups.

Rational Constructions of Modules for Simple Lie Algebras

Author: George B. Seligman

Publisher: American Mathematical Soc.

ISBN: 0821850083

Category: Mathematics

Page: 185

View: 9695

This book is directed to researchers in Lie theory and in the theory of linear algebra, associative or otherwise, and to graduate students who have had some background in one or more of these areas.

Constructions of Lie Algebras and their Modules

Author: George B. Seligman

Publisher: Springer

ISBN: 3540388648

Category: Mathematics

Page: 196

View: 2944

This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.

Extended Affine Lie Algebras and Their Root Systems

Author: Bruce Normansell Allison

Publisher: American Mathematical Soc.

ISBN: 0821805940

Category: Mathematics

Page: 122

View: 6351

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.

Publicationes mathematicae

Author: Kossuth Lajos Tudományegyetem. Matematikai Intézet

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7572

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 804

Homogeneous Banach Algebras

Author: Wang

Publisher: CRC Press

ISBN: 9780824765880

Category: Mathematics

Page: 216

View: 9415

Monographic Series

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category: Monographic series

Page: N.A

View: 4020

(1947-1965).

Author: Nathan Jacobson

Publisher: Birkhauser

ISBN: 9780817634117

Category: Mathematics

Page: 556

View: 1346

(1965-1988).

Author: Nathan Jacobson

Publisher: Birkhauser

ISBN: 9780817634469

Category: Mathematics

Page: 596

View: 529

Groups, Rings and Group Rings

Author: Antonio Giambruno,Cesar Polcino Milies,Sudarshan K. Sehgal

Publisher: CRC Press

ISBN: 9781420010961

Category: Mathematics

Page: 368

View: 2618

This book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.

Mathematical Methods of Classical Mechanics

Author: V.I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 1475720637

Category: Mathematics

Page: 520

View: 4778

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Integration and Cubature Methods

A Geomathematically Oriented Course

Author: Willi Freeden,Martin Gutting

Publisher: CRC Press

ISBN: 1351764756

Category: Mathematics

Page: 501

View: 3697

In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.

Subject Catalog

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 5002

Difference Equations

Theory, Applications and Advanced Topics, Third Edition

Author: Ronald E. Mickens

Publisher: CRC Press

ISBN: 1482230798

Category: Mathematics

Page: 555

View: 4473

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations; nonlinear equations that may be reduced to linear equations; and partial difference equations. New to the Third Edition New chapter on special topics, including discrete Cauchy–Euler equations; gamma, beta, and digamma functions; Lambert W-function; Euler polynomials; functional equations; and exact discretizations of differential equations New chapter on the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences Additional problems in all chapters Expanded bibliography to include recently published texts related to the subject of difference equations Suitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanations.

Computational Algebraic Geometry

Author: Hal Schenck

Publisher: Cambridge University Press

ISBN: 9780521536509

Category: Mathematics

Page: 193

View: 3552

This 2003 book investigates interplay between algebra and geometry. Covers: homological algebra, algebraic combinatorics and algebraic topology, and algebraic geometry.