Capelli identities on algebras with involution or graded involution

Authors: FRANCESCA SAVIELLA BENANTI, ANGELA VALENTI

Abstract: We present recent results about Capelli polynomials with involution or graded involution and their asymptotics. In the associative case, the asymptotic equality between the codimensions of the $T$-ideal generated by the Capelli polynomial of rank $k^2+1$ and the codimensions of the matrix algebra $M_k(F)$ was proved. This result was extended to superalgebras. Recently, similar results have been determined by the authors in the case of algebras with involution and superalgebras with graded involution.

Keywords: Involution, graded involution, Capelli polynomials, codimension

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