Titlebook: Infinite Dimensional Lie Algebras; An Introduction Victor G. Kac Book 1983 Springer Science+Business Media New York 1983 cls.differential e

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Affine Lie algebras: the realization (case k=2 or 3). Application to the classification of finite o polynomial maps from it ℂ. to a simple finite-dimensional Lie algebra with the action of a finite cyclic group. As a side result of this construction we deduce a nice description of the finite order automorphisms of a simple finite-dimensional Lie algebra, and, in particular, the classification of

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Highest weight modules over the Lie algebra g(,),king the category of restricted h-diagonalizable modules (the precise definition is given below). We study the “elementary” objects of this category, the so-called Verma modules, and their connection with irreducible modules. We discuss the problems of irreducibility and complete reducibility in the

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Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restistence of a Ii(A)-invariant positive-definite Hermitian form on .(Λ). Finally, we study the decomposition of .(Λ) with respect to various subalgebras of g(.) and derive an explicit description of the region of convergence of ch.(Λ).

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Infinite Dimensional Lie Algebras978-1-4757-1382-4Series ISSN 0743-1643 Series E-ISSN 2296-505X

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0743-1643 Overview: 978-1-4757-1384-8978-1-4757-1382-4Series ISSN 0743-1643 Series E-ISSN 2296-505X