On Lie algebras associated with representation-finite algebras

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