Algebraic Properties of Codimension Series of PI-Algebras

Autor:	Boumova, Silvia, Drensky, Vesselin
Rok vydání:	2011
Předmět:	Mathematics - Rings and Algebras Mathematics - Combinatorics 05A15 05E10 16R10 20C30
Druh dokumentu:	Working Paper
Popis:	For a PI-algebra R over a field of characteristic 0 let T(R) be the T-ideal of the polynomial identities of R and let c(R,t) be the codimension series of R (i.e., the generating function of the codimension sequence of R). Let A, B and R be PI-algebras such that T(R)=T(A)T(B). We show that if c(A,t) and c(B,t) are rational functions, then c(R,t) is also rational. If c(A,t) is rational and c(B,t) is algebraic, then c(R,t) is also algebraic. The proof is based on the fact that the product of two exponential generating functions behaves as the exponential generating function of the sequence of the degrees of the outer tensor products of two sequences of representations of symmetric groups. Comment: 14 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1111.0319 Zobrazit plný text záznamu View this record from Arxiv