Generalized Centrosymmetric Matrix Algebras Induced by Automorphisms

Let [Formula: see text] be a ring with an automorphism [Formula: see text] of order two. We introduce the definition of [Formula: see text]-centrosymmetric matrices. Denote by [Formula: see text] the ring of all [Formula: see text] matrices over [Formula: see text], and by [Formula: see text] the set of all [Formula: see text]-centrosymmetric [Formula: see text] matrices over [Formula: see text] for any positive integer [Formula: see text]. We show that [Formula: see text] is a separable Frobenius extension. If [Formula: see text] is commutative, then [Formula: see text] is a cellular algebra over the invariant subring [Formula: see text] of [Formula: see text].