On Lie algebras associated with representation-finite algebras

Abstract

Let Λ be a representation-finite C-algebra which has Hall polynomials, with the universal cover Λ~ which is a locally bounded directed C-algebra. In this paper we prove that the Z-Lie algebra L(Λ) associated with Λ which is defined by Riedtmann in [17] and the Z-Lie algebra K(Λ) associated with Λ which is defined by Ringel in [19] are isomorphic. As an application we show that if Λ is a representation-finite (generalized) cluster-tilted algebra or representation-finite trivial extension algebra, then K(Λ). ≅. L(Λ). © 2015 Elsevier Inc.