Cellularity of signed symmetric group algebras

Abstract

In this paper, we introduce signed symmetric group algebras as a symmetric algebras with each edge of basis elements of symmetric group algebra are indexed by the group elements of ℤ2. We establish the generators and its relations for signed symmetric group algebras. Applying, the definition of cellularity of [2], we prove that the signed symmetric group algebras are cellular over the field of characteristic zero. Finally, we find the dimension for the irreducible representations of signed symmetric group algebras over the field of characteristic zero.