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.
Involution, graded involution, Capelli polynomials, codimension
BENANTI, FRANCESCA SAVIELLA and VALENTI, ANGELA
"Capelli identities on algebras with involution or graded involution,"
Turkish Journal of Mathematics: Vol. 46:
5, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss5/2