Complexity of multiplication in commutative group algebras over fields of characteristic 0

Abstract

Let rkA denote the bilinear complexity (also known as rank) of a finite-dimension associative algebra A. Algebras of minimal rank are widely studied from the point of view of bilinear complexity. These are the algebras A for which the Alder-Strassen inequality is satisfied as an equality, i.e., rkA = 2dimA − t, where t is the number of maximum two-sided ideals in A.