ON THE ASYMPTOTICS OF CAPELLI POLYNOMIALS

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Abstract

Abstract. We present old and new results about Capelli polynomials, Z2-graded Capellipolynomials 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 Capellipolynomial of rank m. In the ordinary case (see [33]) it was proved the asymptoticequality between the codimensions of the T -ideal generated by the Capelli polynomialCapk2+1 and the codimensions of the matrix algebra Mk(F ). In [9] this result wasextended 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 dimensionalsuperalgebra. Recently, the authors proved that the ∗-codimensions of a ∗-simple finite dimensional algebra are asymptotically equal to the ∗-codimensions of the T-∗-idealgenerated by the ∗-Capelli polynomials Cap+ M+1 and Cap− L+1, for some fixed naturalnumbers M and L.
Lingua originaleEnglish
Titolo della pubblicazione ospitePolynomial Identities in Algebras
Pagine37-56
Numero di pagine20
Stato di pubblicazionePublished - 2021

All Science Journal Classification (ASJC) codes

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