Algebras and groups defined by permutation relations of alternating type

Ferran Cedó, Eric Jespers, Jan Okniński

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

The class of finitely presented algebras over a field K with a set of generators a1,...,an and defined by homogeneous relations of the form a1a2...an=aσ(1)aσ(2)...aσ(n), where σ runs through Altn, the alternating group of degree n, is considered. The associated group, defined by the same (group) presentation, is described. A description of the Jacobson radical of the algebra is found. It turns out that the radical is a finitely generated ideal that is nilpotent and it is determined by a congruence on the underlying monoid, defined by the same presentation. © 2010 Elsevier Inc.
Original languageEnglish
Pages (from-to)1290-1313
JournalJournal of Algebra
Volume324
DOIs
Publication statusPublished - 1 Sep 2010

Keywords

  • Finitely presented
  • Jacobson radical
  • Primary
  • Secondary
  • Semigroup
  • Semigroup ring
  • Semiprimitive

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