Preprojective algebra structure on skew-group algebras (Q2308290)

The paper under review deals with the pre-projective algebra structure on skew-group algebras and it also treats some interesting questions on that subject. In fact, the results are related to the pre-projective algebra structure on the tensor product of two Koszul bimodule Calabi-Yau algebras. It is proved that such an algebra cannot be endowed with a grading structure as required for a higher pre-projective algebra. Moreover, it is constructed explicitly the bound quiver of the higher pre-projective algebra over a finite-dimensional Koszul algebra of finite global dimension. Besides, it is shown in addition that pre-projective algebras over higher representation-infinite Koszul algebras are derivation-quotient algebras whose relations are given by a superpotential. The described main statements and assertions are subsequently formulated into several theorems which have correct and complete proofs. The author also gives a full bibliography concerning the explored theme.