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 k2 + 1 and the codimensions of the matrix algebra Mk(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.

Francesca Saviella Benanti, Angela Valenti (2022). Capelli identities on algebras with involution or graded involution. TURKISH JOURNAL OF MATHEMATICS, 46(2), 1644-1666 [10.55730/1300-0098.3223].

Capelli identities on algebras with involution or graded involution

Francesca Saviella Benanti
;
Angela Valenti
2022-06-20

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 k2 + 1 and the codimensions of the matrix algebra Mk(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.
20-giu-2022
Settore MAT/02 - Algebra
Francesca Saviella Benanti, Angela Valenti (2022). Capelli identities on algebras with involution or graded involution. TURKISH JOURNAL OF MATHEMATICS, 46(2), 1644-1666 [10.55730/1300-0098.3223].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/545590
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