Rational Constructions Of Modules For Simple Lie Algebras PDF Download
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Author | : George B. Seligman |
Publisher | : American Mathematical Soc. |
Total Pages | : 203 |
Release | : 1981 |
Genre | : Mathematics |
ISBN | : 0821850083 |
Download Rational Constructions of Modules for Simple Lie Algebras Book in PDF, ePub and Kindle
Suitable for 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.
Author | : George B. Seligman |
Publisher | : Springer |
Total Pages | : 203 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540388648 |
Download Constructions of Lie Algebras and their Modules Book in PDF, ePub and Kindle
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.
Author | : Alex J. Feingold |
Publisher | : American Mathematical Soc. |
Total Pages | : 158 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 0821851284 |
Download Spinor Construction of Vertex Operator Algebras, Triality, and $E^{(1)}_8$ Book in PDF, ePub and Kindle
The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining operators for modules of vertex operator algebras yield braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algebras and their generalizations are related to constructions in classical representation theory and shed new light on the classical theory. This book accomplishes several goals. The authors provide an explicit spinor construction, using only Clifford algebras, of a vertex operator superalgebra structure on the direct sum of the basic and vector modules for the affine Kac-Moody algebra Dn(1). They also review and extend Chevalley's spinor construction of the 24-dimensional commutative nonassociative algebraic structure and triality on the direct sum of the three 8-dimensional D4-modules. Vertex operator para-algebras, introduced and developed independently in this book and by Dong and Lepowsky, are related to one-dimensional representations of the braid group. The authors also provide a unified approach to the Chevalley, Greiss, and E8 algebras and explain some of their similarities. A Third goal is to provide a purely spinor construction of the exceptional affine Lie algebra E8(1), a natural continuation of previous work on spinor and oscillator constructions of the classical affine Lie algebras. These constructions should easily extend to include the rest of the exceptional affine Lie algebras. The final objective is to develop an inductive technique of construction which could be applied to the Monster vertex operator algebra. Directed at mathematicians and physicists, this book should be accessible to graduate students with some background in finite-dimensional Lie algebras and their representations. Although some experience with affine Kac-Moody algebras would be useful, a summary of the relevant parts of that theory is included. This book shows how the concepts and techniques of Lie theory can be generalized to yield the algebraic structures associated with conformal field theory. The careful reader will also gain a detailed knowledge of how the spinor construction of classical triality lifts to the affine algebras and plays an important role in the spinor construction of vertex operator algebras, modules, and intertwining operators with nontrivial monodromies.
Author | : Georgia Benkart |
Publisher | : American Mathematical Soc. |
Total Pages | : 352 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0821851195 |
Download Lie Algebras and Related Topics Book in PDF, ePub and Kindle
Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Author | : David Mitzman |
Publisher | : American Mathematical Soc. |
Total Pages | : 170 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 0821850431 |
Download Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras Book in PDF, ePub and Kindle
A revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.
Author | : M.-P. Malliavin |
Publisher | : Springer |
Total Pages | : 347 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540386866 |
Download Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin Book in PDF, ePub and Kindle
Author | : Martin Golubitsky |
Publisher | : American Mathematical Soc. |
Total Pages | : 408 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 0821850601 |
Download Multiparameter Bifurcation Theory Book in PDF, ePub and Kindle
This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature. The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.
Author | : Joel E. Cohen |
Publisher | : American Mathematical Soc. |
Total Pages | : 376 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 082185044X |
Download Random Matrices and Their Applications Book in PDF, ePub and Kindle
Features twenty-six expository papers on random matrices and products of random matrices. This work reflects both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology.
Author | : Jerome Kaminker |
Publisher | : American Mathematical Soc. |
Total Pages | : 334 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 0821850776 |
Download Index Theory of Elliptic Operators, Foliations, and Operator Algebras Book in PDF, ePub and Kindle
Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.
Author | : Robert S. Doran |
Publisher | : American Mathematical Soc. |
Total Pages | : 242 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 0821851276 |
Download Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory Book in PDF, ePub and Kindle
This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Operator Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S Muhly (which will be published in a CBMS Regional Conference Series volume), there were twenty-eight lectures delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, there are over one hundred problems and questions scattered throughout this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory.