On Endomorphs of Right-Symmetric Algebras

A. P. Pozhidaev

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

Abstract

We introduce the notion of endomorph E(A) of a (super) algebra E(A) and prove thatE(A) is a simple (super) algebraif A is not an algebra of scalar multiplication.If A is a right-symmetric (super)algebra then E(A) is right-symmetric as well.Thus, we construct a wide class of simple(right-symmetric) (super)algebras which contains a matrix subalgebra with a common unity.We calculate the derivation algebra of the endomorphof a unital algebra A and the automorphism groupof the simple right-symmetric algebra E(Vn) (the endomorph of a direct sum of fields).

Original languageEnglish
Pages (from-to)859-866
Number of pages8
JournalSiberian Mathematical Journal
Volume61
Issue number5
DOIs
Publication statusPublished - 1 Sep 2020

Keywords

  • 512.57
  • automorphism
  • derivation
  • endomorph
  • left-symmetric algebra
  • pre-Lie algebra
  • right-symmetric algebra
  • simple algebra

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