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Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems

Introduction Generalized Kac-Moody algebras Modular forms Lattices and their Theta-functions The proof of Theorem 1.7 The real simple roots Hyperbolic Lie algeb

This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutati

This book provides the reader with the tools to understand the ongoing classification and construction project of Lie superalgebras. It presents the material in

Koszul rings are graded rings which have played an important role in algebraic topology, noncommutative algebraic geometry and in the theory of quantum groups.