Generalized Centrosymmetric Matrix Algebras Induced by Automorphisms

Abstract

Let R be a ring with an automorphism of order two. We introduce the definition of -centrosymmetric matrices. Denote by Mn(R) the ring of all n×n matrices over R, and by Sn(,R) the set of all -centrosymmetric n×n matrices over R for any positive integer n. We show that Sn(,R) Mn(R) is a separable Frobenius extension. If R is commutative, then Sn(,R) is a cellular algebra over the invariant subring R of R.