## Lie Algebras and Their Representations: A Symposium on Lie Algebras and Representation Theory, January 23-27, 1995, Seoul National University, Seoul, KoreaThis book contains the refereed proceedings of the symposium on Lie algebras and representation theory which was held at Seoul National University (Korea) in January 1995. The symposium was sponsored by the Global Analysis Research Center of Seoul National University. Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area. Consequently, this book can serve both as an introduction to various aspects of the theory of Lie algebras and their representations and as a good reference work for further research. |

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### Contents

1 | |

Lie Theory over Commutative Rings and Lifting Invariant Forms | 47 |

Polynomial Representations of Frobenius Kernels of GL2 | 57 |

Homological Topics in the Representation Theory of Restricted Lie Algebras | 69 |

An Exposition of Generalized KacMoody Algebras | 121 |

Root Multiplicities of Graded Lie Algebras | 161 |

Similarity of Crystal Bases | 177 |

Some Topics on the Representation Theory of Generalized KacMoody Algebras | 187 |

Complexity and Support Varieties for Finite Dimensional Algebras | 201 |

Quasiparticle Structure in Solvable Vertex Models | 219 |

### Other editions - View all

Lie Algebras and Their Representations: A Symposium on Lie Algebras and ... Seok-Jin Kang,Myung-Hwan Kim,Insok Lee No preview available - 1996 |

### Common terms and phrases

abelian algebraic group bilinear form Borcherds Brauer algebra centralizer algebra character formula commutative Corollary corresponding crystal decomposition defined definition denote diagram dimension dimensional restricted Lie direct sum elements finite dimensional restricted free Lie algebra Frobenius GKM algebras gš-module graded graded Lie algebras highest weight module homology Hopf algebra indecomposable injective integer invariant irreducible highest weight irreducible representations isomorphism Kac-Moody algebras Lemma Math Mathematics matrix Monster Lie algebra non-Steinberg blocks one-dimensional p-nilpotent partition polynomial projective proof Proposition quantum groups representation theory resp restricted cohomology restricted L-module restricted Lie algebra result semisimple sequence simple Lie algebras simple modules simple restricted simple roots subset supersolvable restricted Lie support varieties symmetric tensor product Theorem Torp(L torus universal enveloping algebra Verma module vertex Weyl group X)-module