Koszul algebras and the Gorenstein condition

Non commutative versions of regular algebras appear naturally in representation theory as the Yoneda algebras of selfinjective Koszul algebras, they have been studied in [4], [10], [11]. Here we extend these notions by considering algebras such that some of the simple satisfy the Gorenstein condition [1], [9], [12]. When they are Koszul, we study the corresponding Yoneda algebras, examples of such algebras will be the Auslander algebra, the preprojective algebra and selfinjective algebras of radical cube zero of infinite representation type. We will prove that by taking tensor products we can construct new algebras satisfying the Gorenstein condition.