Group algebras and semigroup algebras defined by permutation relations of fixed length

Ferran Cedó, Eric Jespers, Georg Klein

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2016 World Scientific Publishing Company. Let H be a subgroup of Symn, the symmetric group of degree n. For a fixed integer l ≥ 2, the group G presented with generators x1, x2, . . . ,xn and with relations x1x2. . . xl = xσ(i1)xσ(i2) . . . xσ(il), where σ runs through H, is considered. It is shown that G has a free subgroup of finite index. For a field K, properties of the algebra K[G] are derived. In particular, the Jacobson radical J (K[G]) is always nilpotent, and in many cases the algebra K[G] is semiprimitive. Results on the growth and the Gelfand.Kirillov dimension of K[G] are given. Further properties of the semigroup S and the semigroup algebra K[S] with the same presentation are obtained, in case S is cancellative. The Jacobson radical is nilpotent in this case as well, and sufficient conditions for the algebra to be semiprimitive are given.
Original languageEnglish
Article number1650037
JournalJournal of Algebra and Its Applications
Volume15
Issue number2
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Group algebra
  • Jacobson radical
  • semigroup algebra
  • semiprimitive
  • symmetric presentation

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