Polynomial identities with involution, superinvolutions and the Grassmann envelope

Eli Aljadeff*, Antonio Giambruno, Yakov Karasik

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.

Original languageEnglish
Pages (from-to)1843-1857
Number of pages15
JournalProceedings of the American Mathematical Society
Volume145
Issue number5
DOIs
StatePublished - 2017

Keywords

  • Grassmann algebra
  • Involution
  • Polynomial identity
  • Superinvolution

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