The APR Tilted Algebras Of The Truncated Algebras Of The McKay Quivers Of Abelian Subgroup Of GL(3,C)

Recently, Guo Jinyun have characterized a class of finite abelian groups McKay quiver Q(m), which is a class of limited complexity of the self-injective algebras. We discuss its truncated algebras and APR tilting theories in m=3case. This paper proves that the truncated algebras of Q(3) are isomorphic, and depicts the truncated algebra of the McKay quiver Q(3), gives the mor-phism relationship of indecomposable projective modules and indecomposable injective modules. We also study the tilt theory of the truncated algebras, in particular, we study the APR tilting modules and tilted algebra. We por-trayed the quiver of APR tilted algebra, and we have the conclusion that the results of the APR tilted algebra and multiple single-point expansion:the APR tilted algebra of the truncated algebra and multiple single-point expansion of structure can be exchanged.