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| Author | : David Mitzman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 170 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 0821850431 |
A 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. |
| Total Pages | : 113 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 0821825275 |
We 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. |
| Total Pages | : 226 |
| Release | : 2011 |
| Genre | : Nonassociative rings |
| ISBN | : 082185237X |
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 | : Daniel J. Britten |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 398 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 9780821860090 |
As 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. |
| Total Pages | : 161 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 0821824236 |
| Author | : Roger William Carter |
| Publisher | : Cambridge University Press |
| Total Pages | : 662 |
| Release | : 2005-10-27 |
| Genre | : Mathematics |
| ISBN | : 9780521851381 |
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
| Author | : Katrina Barron |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 274 |
| Release | : 2017-08-15 |
| Genre | : Lie algebras |
| ISBN | : 1470426668 |
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
| Author | : Eric Grinberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : 0821851209 |
Contains 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. |
| Total Pages | : 290 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 0821851225 |
High 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. |
| Total Pages | : 96 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 0821850482 |
The 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
