caa a22 4500 606160574 CHVBK 20210128100630.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10468-014-9490-y doi (NATIONALLICENCE)springer-10.1007/s10468-014-9490-y Benanti Francesca Dipartimento di Matematica ed Informatica, Università di Palermo, via Archirafi, 34, 90123, Palermo, Italy aut Asymptotics for Graded Capelli Polynomials [Elektronische Daten] [Francesca Benanti] The finite dimensional simple superalgebras play an important role in the theory of PI-algebras in characteristic zero. The main goal of this paper is to characterize the T 2-ideal of graded identities of any such algebra by considering the growth of the corresponding supervariety. We consider the T 2-ideal Γ M+1,L+1 generated by the graded Capelli polynomials C a p M+1[Y,X] and C a p L+1[Z,X] alternanting on M+1 even variables and L+1 odd variables, respectively. We prove that the graded codimensions of a simple finite dimensional superalgebra are asymptotically equal to the graded codimensions of the T 2-ideal Γ M+1,L+1, for some fixed natural numbers M and L. In particular c n sup ( Γ k 2 + l 2 + 1 , 2 kl + 1 ) ≃ c n sup ( M k , l ( F ) ) $$c^{sup}_{n}(\Gamma_{k^{2}+l^{2}+1,2kl+1})\simeq c^{sup}_{n}(M_{k,l}(F))$$ and c n sup ( Γ s 2 + 1 , s 2 + 1 ) ≃ c n sup ( M s ( F ⊕ tF ) ) . $$c^{sup}_{n}(\Gamma_{s^{2}+1,s^{2}+1})\simeq c^{sup}_{n}(M_{s}(F\oplus tF)).$$ These results extend to finite dimensional superalgebras a theorem of Giambruno and Zaicev [6] giving in the ordinary case the asymptotic equality c n sup ( Γ k 2 + 1 , 1 ) ≃ c n sup ( M k ( F ) ) $$c^{sup}_{n}(\Gamma_{k^{2}+1,1})\simeq c^{sup}_{n}(M_{k}(F)) $$ between the codimensions of the Capelli polynomials and the codimensions of the matrix algebra M k (F). Springer Science+Business Media Dordrecht, 2014 Superalgebras nationallicence Polynomial identities nationallicence Codimensions nationallicence Growth nationallicence Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 221-233 1386-923X 18:1<221 2015 18 10468 https://doi.org/10.1007/s10468-014-9490-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9490-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Benanti Francesca Dipartimento di Matematica ed Informatica, Università di Palermo, via Archirafi, 34, 90123, Palermo, Italy aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 221-233 1386-923X 18:1<221 2015 18 10468