Serre relations and Gröbner-Shirshov bases for simple lie algebras I

L. A. Bokut, A. A. Klein

Research output: Contribution to journalArticlepeer-review

Abstract

A Gröbner-Shirshov basis for the Lie algebra An, abstractly defined by generators hi,xi,yi, i = 1, . . . ,n and the Serre relations for the Cartan matrix An, over a field k of characteristic ≠ 2 is constructed. It consists of the Serre relations for An together with the following relations: [[xi+jxi+j-1 ⋯ xi-1]xi+j-1], [[xi+j ⋯ xi] [xi+j ⋯ xixi-1]] with j ≥ 1, i ≥ 2, i + j ≤ n and the same relations for y1, . . . , yn, where by [z1z2 ⋯ zm] we mean [z1[z2 ⋯ Zm]]. As an application we get a direct proof that An, as defined, is isomorphic to sln+1(k).

Original languageEnglish
Pages (from-to)389-400
Number of pages12
JournalInternational Journal of Algebra and Computation
Volume6
Issue number4
DOIs
StatePublished - Aug 1996

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