TWISTED GROUP ALGEBRAS SATISFYING A GENERALIZED POLYNOMIAL IDENTITY

Abstract

If K^t [G] is a twisted group algebra satisfying a nondegenerate multilinear generalized polynomial identity f(ζ₁,ζ₂,…, ζ _n ) = 0, then we show that G has certain normal subgroups of finite index which can be viewed as being almost central. For example, there exists H ◃ G with |G:H| · |H′| bounded by a fixed function of the support sizes of the nonzero K^t [G]-terms involved in f. Indeed, we obtain a more precise version of this result, with the structure of H depending upon the specific twisting in the group algebra. We then go on to determine necessary and sufficient conditions for K^t [G] to satisfy such an identity.

Keywords:

• 2000 Mathematics Subject Classification: 16S34, 16R50

ACKNOWLEDGMENT

The author's research was supported in part by NSF Grant DMS-9820271.