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EnglishAbstract. We present old and new results about Capelli polynomials, Z2-graded Capelli polynomials and Capelli polynomials with involution and their asymptotics. Let Capm = Pσ2Sm (sgnσ)tσ(1)x1tσ(2) · · · tσ(m−1)xm−1tσ(m) be the m-th Capelli polynomial of rank m. In the ordinary case (see [33]) it was proved the asymptotic equality between the codimensions of the T -ideal generated by the Capelli polynomial Capk2+1 and the codimensions of the matrix algebra Mk(F ). In [9] this result was extended to superalgebras proving that the Z2-graded codimensions of the T2-ideal generated by the Z2-graded Capelli polynomials Cap0 M+1 and Cap1 L+1 for some fixed M, L, are asymptotically equal to the Z2-graded codimensions of a simple finite dimensional superalgebra. Recently, the authors proved that the ∗-codimensions of a ∗-simple finite dimensional algebra are asymptotically equal to the ∗-codimensions of the T-∗-ideal generated by the ∗-Capelli polynomials Cap+ M+1 and Cap− L+1, for some fixed natural numbers M and L.
Francesca Saviella Benanti, & Angela Valenti (2021). ON THE ASYMPTOTICS OF CAPELLI POLYNOMIALS. In O. Di Vincenzo, & Giambruno A. (a cura di), Polynomial Identities in Algebras (pp. 37-56). Springer.
| Data di pubblicazione: | 2021 | |
| Titolo: | ON THE ASYMPTOTICS OF CAPELLI POLYNOMIALS | |
| Autori: | ||
| Citazione: | Francesca Saviella Benanti, & Angela Valenti (2021). ON THE ASYMPTOTICS OF CAPELLI POLYNOMIALS. In O. Di Vincenzo, & Giambruno A. (a cura di), Polynomial Identities in Algebras (pp. 37-56). Springer. | |
| Abstract: | Abstract. We present old and new results about Capelli polynomials, Z2-graded Capelli polynomials and Capelli polynomials with involution and their asymptotics. Let Capm = Pσ2Sm (sgnσ)tσ(1)x1tσ(2) · · · tσ(m−1)xm−1tσ(m) be the m-th Capelli polynomial of rank m. In the ordinary case (see [33]) it was proved the asymptotic equality between the codimensions of the T -ideal generated by the Capelli polynomial Capk2+1 and the codimensions of the matrix algebra Mk(F ). In [9] this result was extended to superalgebras proving that the Z2-graded codimensions of the T2-ideal generated by the Z2-graded Capelli polynomials Cap0 M+1 and Cap1 L+1 for some fixed M, L, are asymptotically equal to the Z2-graded codimensions of a simple finite dimensional superalgebra. Recently, the authors proved that the ∗-codimensions of a ∗-simple finite dimensional algebra are asymptotically equal to the ∗-codimensions of the T-∗-ideal generated by the ∗-Capelli polynomials Cap+ M+1 and Cap− L+1, for some fixed natural numbers M and L. | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-3-030-63111-6 | |
| Settore Scientifico Disciplinare: | Settore MAT/02 - Algebra | |
| Appare nelle tipologie: | 2.01 Capitolo o Saggio |
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