Irreducible highest weight representations of the simple n-Lie algebra

D.M. Balibanu; J.W. van de Leur

doi:10.1007/s00031-012-9189-2

Irreducible highest weight representations of the simple n-Lie algebra

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

A. Dzhumadil’daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra

Original language	English
Pages (from-to)	593-613
Number of pages	21
Journal	Transformation Groups
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s00031-012-9189-2
Publication status	Published - 2012

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abstract = "A. Dzhumadil{\textquoteright}daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra",

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AB - A. Dzhumadil’daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra

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DO - 10.1007/s00031-012-9189-2

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JO - Transformation Groups

JF - Transformation Groups

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Irreducible highest weight representations of the simple n-Lie algebra

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