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Lie Algebras, Vertex Operator Algebras and Their Applications
Edited by: Yi-Zhi Huang, Rutgers University, Piscataway, NJ, and Kailash C Misra, North Carolina State University, Raleigh, NC
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Contemporary Mathematics
2007; 474 pp; softcover
Volume: 442
ISBN-10: 0-8218-3986-1
ISBN-13: 978-0-8218-3986-7
List Price: US$133
Member Price: US$106.40
Order Code: CONM/442
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The articles in this book are based on talks given at the international conference "Lie algebras, vertex operator algebras and their applications", in honor of James Lepowsky and Robert Wilson on their sixtieth birthdays, held in May of 2005 at North Carolina State University. Some of the papers in this volume give inspiring expositions on the development and status of their respective research areas. Others outline and explore the challenges as well as the future directions of research for the twenty-first century. The focus of the papers in this volume is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.

This book is useful for graduate students and researchers in mathematics and mathematical physics who want to be introduced to different areas of current research or explore the frontiers of research in the areas mentioned above.

Readership

Graduate students and research mathematicians interested in lie algebras, their representations, and generalizations.

Table of Contents

Lie algebras and related topics
  • K. Baur and N. Wallach -- A class of gradings of simple Lie algebras
  • S. Berman and J. Morita -- Conjugacy results for the Lie algebra \(\mathfrak{sl}_2\) over an algebra which is a UFD
  • V. Chari and A. Moura -- Kirillov-Reshetikhin modules associated to \(G_2\)
  • R. Farnsteiner -- Support spaces and Auslander-Reiten components
  • J. Feldvoss -- On the cohomology of modular Lie algebras
  • H. Garland -- Eisenstein series on loop groups: Maass-Selberg relations 4
  • A. Hoshino -- Generalized Littlewood-Richardson rule for exceptional Lie algebras \(E_6\) and \(F_4\)
  • D. Nacin -- An introduction to \(Q_n\) and its graph related quotients
  • T. Nakashima -- Affine geometric crystal of type \(G^{(1)}_2\)
  • F. F. Nichita and D. Parashar -- New constructions of Yang-Baxter systems
  • V. Retakh, S. Serconek, and R. L. Wilson -- Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials
  • A. Savage -- Geometric and combinatorial realizations of crystals of enveloping algebras
  • H. Strade -- Lie algebras of small dimension
Vertex (operator) algebras and related topics
  • I. I. Anguelova -- Symmetric polynomials and \(H_D\)-quantum vertex algebras
  • M. J. Bergvelt -- \(H_T\)-vertex algebras
  • C. Calinescu -- On intertwining operators and recursions
  • C. Dong and C. Jiang -- Representations of vertex operator algebras
  • J. Fuchs -- On non-semisimple fusion rules and tensor categories
  • K. Hubbard -- The duality between vertex operator algebras and coalgebras, modules and comodules
  • J. Lepowsky -- Some developments in vertex operator algebra theory, old and new
  • H. Li -- Twisted modules and quasi-modules for vertex operator algebras
  • G. Mason and M. P. Tuite -- Chiral algebras and partition functions
  • A. Milas -- Modular forms and almost linear dependence of graded dimensions
  • M. Primc -- \((k,r)\)-Admissible configurations and intertwining operators
  • Z. Qin and W. Wang -- Hilbert schemes of points on the minimal resolution and soliton equations
  • C. Schweigert, J. Fuchs, and I. Runkel -- Twining characters and Picard groups in rational conformal field theory
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