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Koszul and quasi-Koszul algebras obtained by tilting

R. M. Aquino, E. L. Green, E. N. Marcos (2002)

Colloquium Mathematicae

Given a finite-dimensional algebra, we present sufficient conditions on the projective presentation of the algebra modulo its radical for a tilted algebra to be a Koszul algebra and for the endomorphism ring of a tilting module to be a quasi-Koszul algebra. One condition we impose is that the algebra has global dimension no greater than 2. One of the main techniques is studying maps between the direct summands of the tilting module. Some applications are given. We also show that a Brenner-Butler...

Koszul duality for N-Koszul algebras

Roberto Martínez-Villa, Manuel Saorín (2005)

Colloquium Mathematicae

The correspondence between the category of modules over a graded algebra and the category of graded modules over its Yoneda algebra was studied in [8] by means of A algebras; this relation is very well understood for Koszul algebras (see for example [5],[6]). It is of interest to look for cases such that there exists a duality generalizing the Koszul situation. In this paper we will study N-Koszul algebras [1], [7], [9] for which such a duality exists.

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