On $ n $-slice algebras and related algebras.

The -slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of -slice algebras via their -preprojective algebras and the trivial extensions of their quadratic duals. One can always relate tame -slice algebras to the McKay quiver of a finite subgroup of . In the case of , we describe the relations for the -slice algebras related to the McKay quiver of finite Abelian subgroups of and of the finite subgroups obtained from embedding into . [ABSTRACT FROM AUTHOR]