Asymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras

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Abstract

We consider associative PI-algebras over a field of characteristic zero. Themain goal of the paper is to prove that the codimensions of a verbally primealgebra [11] are asymptotically equal to the codimensions of the T-ideal generatedby some Amitsur’s Capelli-type polynomials E¤M;L [1]. In particular weprove thatcn(Mk(G)) '' cn(E¤k2;k2 )andcn(Mk;l(G)) '' cn(E¤k2+l2;2kl);where G is the Grassmann algebra. These results extend to all verbally primePI-algebras a theorem of A.Giambruno and M.Zaicev [9] giving the asymptoticequalitycn(Mk(F)) '' cn(E¤k2;0)between the codimensions of the matrix algebra Mk(F) and the Capelli polynomials.
Lingua originaleEnglish
pagine (da-a)73-91
Numero di pagine19
RivistaIsrael Journal of Mathematics
Volume156
Stato di pubblicazionePublished - 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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