On the Right-Symmetric Algebras with a Unital Matrix Subalgebra

A. P. Pozhidaev, I. P. Shestakov

Research output: Contribution to journalArticlepeer-review

Abstract

Under study are the right-symmetric algebras over a field $ F $which possess a “unital” matrix subalgebra $ M_{n}(F) $.We classify all these finite-dimensional right-symmetric algebras $ {\mathcal{A}}=W\oplus M_{2}(F) $ in the case when $ W $ is anirreducible module over $ sl_{2}(F) $.

Original languageEnglish
Pages (from-to)138-147
Number of pages10
JournalSiberian Mathematical Journal
Volume62
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • 512.57
  • Koszul–Vinberg algebra
  • left-symmetric algebra
  • pre-Lie algebra
  • right-symmetric algebra
  • simple algebra

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