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## Rational methods in Lie algebras

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

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

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

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

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

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.
## Lecture notes in pure and applied mathematics

## Publicationes mathematicae

## Bulletin of the American Mathematical Society

## Subject Guide to Books in Print

## Mathematics of Cell Electrophysiology

## Hyperbolic Differential Operators And Related Problems

Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.
## Homogeneous Banach Algebras

## Monographic Series

## (1947-1965).

## (1965-1988).

## Groups, Rings and Group Rings

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.
## Subject Catalog

## Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras.
## Noetherian Semigroup Algebras

Here is a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These results are applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have recently been intensively studied. The focus is on the interplay between combinatorics and algebraic structure. Mathematical physicists will find this work interesting for its attention to applications of the Yang-Baxter equation.

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Author: George B. Seligman

Publisher: Marcel Dekker Inc

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Category: Mathematics

Page: 346

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*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

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*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

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Publisher: Springer

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*An Index to the Publishers' Trade List Annual*

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Publisher: CRC Press

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ISBN: 9780817634117

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

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Author: Stefaan Caenepeel,Gigel Militaru,Shenglin Zhu

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ISBN: 1402058101

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