Construction of Representation-Finite Selfinjective Artin Algebras of Class B., and C.

In this paper, we discuss the representation-finite selfinjective artin algebras of class B, and C, and obtain the following main results: For any field k, let A be a representation-finite selfinjective artin algebras of class B. o C. over k. (a) We give the configuration of ZB., and ZC.. (b) We show that A is standard. (c) Under the condition of k being a perfect field, we describe A by bourden k-species and show that A is a finite covering of the trivial extension of some tilted algebra of type B., or C.