Ph.D Thesis
Ph.D Student Yuval Shpigelman On the Codimension Growth of G-Graded Algebras Department of Mathematics Full Professor Aljadeff Eli

Abstract

Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G.

In the first part of the thesis we show that there exist nonnegative numbers a1 , a2 , a half integer b and an integer l such that  a1 n?b ?ln ? < cnG(W) <  a2 n?b ?ln . Furthermore, if W has a unit then the asymptotic behavior of cnG(W)  is  an?b ?ln.   The nonnegative integer l is called the exponent of W, and denoted by expG(W). If W is finite dimensional, then there is an algebraic interpretation to the exponent as a subalgebra of the semi-simple part of W.

In the second part of the thesis, which is a joint work withYakov Karasik, we find the interpretation of the half integer b in case that W is a finite dimensional G-simple F-algebra. We prove that cnG(W)~ an?b ?ln  where b=(dimWe -1)/2 and a is yet to be found in the general G-simple  case. In the special case where W is the algebra of mXm matrices with an arbitrary elementary G-grading we manage to calculate a explicitly