The polynomial part of the codimension growth of affine PI algebras

TY - JOUR

T1 - The polynomial part of the codimension growth of affine PI algebras

AU - Aljadeff, Eli

AU - Janssens, Geoffrey

AU - Karasik, Yakov

N1 - Publisher Copyright: © 2017 Elsevier Inc.

PY - 2017/3/17

Y1 - 2017/3/17

N2 - Let F be a field of characteristic zero and W an associative affine F-algebra satisfying a polynomial identity (PI). The codimension sequence {cn(W)} associated to W is known to be of the form Θ(ntdn), where d is the well known PI-exponent of W. In this paper we establish an algebraic interpretation of the polynomial part (the constant t) by means of Kemer's theory. In particular, we show that in case W is a basic algebra (hence finite dimensional), t=q−d2+s, where q is the number of simple component in W/J(W) and s+1 is the nilpotency degree of J(W) (the Jacobson radical of W). Thus proving a conjecture of Giambruno.

AB - Let F be a field of characteristic zero and W an associative affine F-algebra satisfying a polynomial identity (PI). The codimension sequence {cn(W)} associated to W is known to be of the form Θ(ntdn), where d is the well known PI-exponent of W. In this paper we establish an algebraic interpretation of the polynomial part (the constant t) by means of Kemer's theory. In particular, we show that in case W is a basic algebra (hence finite dimensional), t=q−d2+s, where q is the number of simple component in W/J(W) and s+1 is the nilpotency degree of J(W) (the Jacobson radical of W). Thus proving a conjecture of Giambruno.

KW - Codimension sequence

KW - Kemer polynomials

KW - Polynomial identity

UR - http://www.scopus.com/inward/record.url?scp=85012296942&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2017.01.022

DO - 10.1016/j.aim.2017.01.022

M3 - 文章

AN - SCOPUS:85012296942

SN - 0001-8708

VL - 309

SP - 487

EP - 511

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -