Automorphisms of the endomorphism semigroup of a free associative algebra

A. Belov-Kanel, A. Berzins, R. Lipyanski

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Let A be the variety of associative algebras over a field K and A = K(x1, . . ., xn) be a free associative algebra in the variety A freely generated by a set X = {x1, . . ., xn}, End A the semigroup of endomorphisms of A, and Aut End A the group of automorphisms of the semigroup End A. We prove that the group Aut End A is generated by semi-inner and mirror automorphisms of End A. A similar result is obtained for the automorphism group Aut ao, where ac is the subcategory of finitely generated free algebras of the variety A. The later result solves Problem 3.9 formulated in [17].

Original languageEnglish
Pages (from-to)923-939
Number of pages17
JournalInternational Journal of Algebra and Computation
Volume17
Issue number5-6
DOIs
StatePublished - 2007

Keywords

  • Free algebra
  • Semi-inner automorphism
  • Variety of associative algebras

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