On the Codimension Sequence of G-Simple Algebras

2013/12/15 by Karasik, Yaakov, Shpigelman, Yuval
#16R10 (Primary) 16R30 #16W50 #16Z05 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1312.4167

Abstract

In the 80's, Regev, using results of Formanek, Procesi and Razmyslov in invariant theory and Hilbert series', determined asymptotically the codimension sequence of mXm matrices over an algebraically closed field of characteristic zero. Inspired by Regev's ideas, we found that the asymptotics of c_n^G(A), the G graded codimension sequence of a finite dimensional G simple algebra A, is equal to αn^\frac1-dim(A_e)2(dim(A)ⁿ (this was conjectured by E.Aljadeff, D.Haile and M. Natapov), where αis not yet determined number. Moreover, in the case where A is the algebra of mXm matrices with an arbitrary elementary G-grading we also manged to calculate α.

Related

• The Asymptotic Behavior of the Codimension Sequence of Affine G - Graded Algebras
• Multialternating graded polynomials and growth of polynomial identities
• Varieties of graded W-algebras and asymptotic behavior of codimension growth
• Group graded algebras and varieties with quadratic codimension growth
• Graded algebras with homogeneous involution and varieties of almost polynomial growth