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Star-polynomial identities: Computing the exponential growth of the codimensions

  • Autori: Giambruno,A,; Polcino Milies, C; Valenti, A
  • Anno di pubblicazione: 2017
  • Tipologia: Articolo in rivista (Articolo in rivista)
  • OA Link:


Can one compute the exponential rate of growth of the ∗-codimensions of a PI-algebra with involution ∗ over a field of characteristic zero? It was shown ithat any such algebra A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth exp∗(A) of any PI-algebra A with involution. It turns out that exp∗(A) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.