On a Generalized Matrix Algebra over Frobenius Algebra

Abstract

Let $A$ be a Frobenius $k$-algebra. The matrix algebra $R=\begin{pmatrix}A & _AA_k\\[1mm]_kA_A & k\end{pmatrix}$ is called a generalized matrix algebra over a Frobenius algebra $A$. In this paper we show that $R$ is also a Frobenius algebra.