Search results for " Exponential growth"

The exponent for superalgebras with superinvolution

2018

Abstract Let A be a superalgebra with superinvolution over a field of characteristic zero and let c n ⁎ ( A ) , n = 1 , 2 , … , be its sequence of ⁎-codimensions. In [6] it was proved that such a sequence is exponentially bounded. In this paper we capture this exponential growth for finitely generated superalgebras with superinvolution A over an algebraically closed field of characteristic zero. We shall prove that lim n → ∞ ⁡ c n ⁎ ( A ) n exists and it is an integer, denoted exp ⁎ ⁡ ( A ) and called ⁎-exponent of A. Moreover, we shall characterize finitely generated superalgebras with superinvolution according to their ⁎-exponent.