2-APR Tiled Algebras Of Truncated Algebras Of McKay Quivers

Recently, Guo has introduced the truncated algebra of self-injective algebra and describe the McKay quiver Q(m) of finite abelian subgroup of Gl(3, C). In this paper, we study the2-APR tilting module and tilted algebras of truncated algebras of Q(3).Firstly,we prove that each of the truncated algebras of Q(m) are isomorphic,then we have more detailed characterization on the truncated algebras of Q(3) and we get the morphism relationship between indecomposable projective modules and indecomposable injective modules.Secondly,We prove that the trun-cated algebras of Q(3) exist2-APR tilting module, and obtain that the quiver of2-APR tilted algebras is the same with the quiver of the truncated algebras which is effected with τ mutation. Finally,we take the McKay quiver of G(3)=(Z/nZ)3as an example and discuss its2-APR tilting.