Polynomial growth and identities of superalgebras and star-algebras

Abstract

We study associative algebras with 1 endowed with an automorphism or antiautomor-\ud phism ' of order 2, i.e., superalgebras and algebras with involution. For any fixed k >=1,\ud we construct associative '-algebras whose '-codimension sequence is given asymptoti-\ud cally by a polynomial of degree k whose leading coefficient is the largest or smallest possi-\ud ble

On algebras of polynomial codimension growth

“…Much effort has been put into the study of varieties V of polynomial growth, i.e., such that c n (V) is polynomially bounded [5,12,[17][18][19][20][21].…”

Varieties of superalgebras of almost polynomial growth

“…Let A ∈ var gr (G gr k ) and suppose that c gr n (A) ≈ qn k , for some q > 0. We shall prove that A ∼ T 2 [14,Theorem 3.4].) Let k 2.…”

Codimensions of star-algebras and low exponential growth

“…, is the dimension of the space of multilinear * -polynomials in n fixed variables in the corresponding relatively free algebra with involution of countable rank. Such sequence has been extensively studied (see [8,15,16,17,18,19] ) but it turns out that it can be explicitly computed only in very few cases. In case A is a PI-algebra, i.e, it satisfies a non trivial polynomial identity, it was proved in [9] that, as in the ordinary case, c * n (A), n = 1, 2, .…”