Exponential Codimension Growth of PI Algebras: An Exact Estimate

Eventual arm and leg widths in cocharacters of P. I. Algebras

“…Our proof is an extension of the work of Giambruno and Zaicev in [4], which in turn is based on the work of Kemer. Given any p.i.…”

Asymptotics for Amitsur's Capelli-type polynomials and verbally prime PI-algebras

“…Also granting B i and C are simple superalgebras we obtain q = 1 and can assume B 1 ∼ = C. 2 and G(A) corresponds to the hook H(k 2 + l 2 , 2kl) for l = 0 (see [7]), we have k 1 = k, and l 1 = l. Then…”

“…Hence there exist constants α, β such that c n (A) ≤ αβ n for any n ≥ 1. It was recently proved by Giambruno and Zaicev, in [6] and [7], that for a P I-algebra A exp(A) = lim exists and is an integer; exp(A) is called the PI-exponent of the algebra A. For the verbally prime algebras we have (see [2], [14], [7])…”

“…The following relations between the exponent of the Capelli-type polynomials and the exponent of the verbally prime algebras are well known (see [3], [7])…”

Целочисленность Экспонент Роста Тождеств Конечномерных Алгебр Ли

“…В свое время Амицуром была высказана гипоте за, что ЕХР (А) всегда существует и является целым числом. Недавно эта гипотеза была подтверждена в работах [11], [12].…”