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Author: David Mitzman
Publisher: American Mathematical Soc.
Published: 1985
Total Pages: 170
ISBN-13: 0821850431
DOWNLOAD EBOOKA revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.
Author: Shari A. Prevost
Publisher: American Mathematical Soc.
Published: 1992
Total Pages: 113
ISBN-13: 0821825275
DOWNLOAD EBOOKWe present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.
Author: Erhard Neher
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 226
ISBN-13: 082185237X
DOWNLOAD EBOOKLie 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: Daniel J. Britten
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 398
ISBN-13: 9780821860090
DOWNLOAD EBOOKAs the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.
Author: Marly Mandia
Publisher: American Mathematical Soc.
Published: 1987
Total Pages: 161
ISBN-13: 0821824236
DOWNLOAD EBOOKAuthor: Roger William Carter
Publisher: Cambridge University Press
Published: 2005-10-27
Total Pages: 662
ISBN-13: 9780521851381
DOWNLOAD EBOOKThis book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author: Eric Grinberg
Publisher: American Mathematical Soc.
Published: 1990
Total Pages: 266
ISBN-13: 0821851209
DOWNLOAD EBOOKContains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. This book features articles that range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis.
Author: Nancy Flournoy
Publisher: American Mathematical Soc.
Published: 1991
Total Pages: 290
ISBN-13: 0821851225
DOWNLOAD EBOOKHigh dimensional integration arises naturally in two major sub-fields of statistics: multivariate and Bayesian statistics. Indeed, the most common measures of central tendency, variation, and loss are defined by integrals over the sample space, the parameter space, or both. Recent advances in computational power have stimulated significant new advances in both Bayesian and classical multivariate statistics. In many statistical problems, however, multiple integration can be the major obstacle to solutions. This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Statistical Multiple Integration, held in June 1989 at Humboldt State University in Arcata, California. The conference represents an attempt to bring together mathematicians, statisticians, and computational scientists to focus on the many important problems in statistical multiple integration. The papers document the state of the art in this area with respect to problems in statistics, potential advances blocked by problems with multiple integration, and current work directed at expanding the capability to integrate over high dimensional surfaces.
Author: James Lepowsky
Publisher: American Mathematical Soc.
Published: 1985
Total Pages: 96
ISBN-13: 0821850482
DOWNLOAD EBOOKThe affine Kac-Moody algebra $A_1 DEGREES{(1)}$ has served as a source of ideas in the representation theory of infinite-dimensional affine Lie algebras. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1 DEGREES{(1)}$-modules in the homogeneou
Author: Shrawan Kumar
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 613
ISBN-13: 1461201055
DOWNLOAD EBOOKKac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.
