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

Risultato della ricerca: Article

1 Citazione (Scopus)

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

Fingerprint

Codimension
Algebra
Polynomial
Grassmann Algebra
Matrix Algebra
Zero
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cita questo

@article{108da999a1d84990b8e7f5463a6f197c,
title = "Asymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras",
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.",
author = "Benanti, {Francesca Saviella} and Irina Sviridova and Irina Sviridova",
year = "2006",
language = "English",
volume = "156",
pages = "73--91",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York",

}

TY - JOUR

T1 - Asymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras

AU - Benanti, Francesca Saviella

AU - Sviridova, Irina

AU - Sviridova, Irina

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/20475

M3 - Article

VL - 156

SP - 73

EP - 91

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -