Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778726 | Advances in Mathematics | 2017 | 25 Pages |
Abstract
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 Î(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=qâd2+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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Eli Aljadeff, Geoffrey Janssens, Yakov Karasik,