In this article we introduce the notion of multi-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, as a generalization of the notion of (generalized) Koszul algebras defined ...

The relationship between an algebra and its associated monomial algebra is investigated when at least one of the algebras is d-Koszul It is shown that an algebra which has a reduced Grobnerbasis that is composed of homogeneous ...

We present a calculus that is well-adapted to homogeneous quadratic algebras. We define this calculus on Koszul cohomology - resp. homology - by cup products - resp. cap products. The Koszul homology and cohomology are ...

In this paper, we study the derived categories of a Koszul algebra and its Yoneda algebra to determine when those categories are triangularly equivalent. We prove that the simply connected Koszul algebras are derived ...

In this article we introduce the notion of multi-Koszul algebra for the case of a nonnegatively graded connected algebra with a finite number of generators of degree 1 and with a finite number of relations, as a generalization ...

Abstract. In the schematic approach to non-commutative algebraic geometry arises some important classes of non-commutative algebras like Koszul algebras, Artin-Schelter regular algebras, Calabi-Yau algebras, and closely ...

The aim of this work is to introduce the class of finitely semi-graded algebras which is a generalization of finitely graded algebras generated in degree one, and include important examples whithin the skew P BW extensions. ...

In this article we establish an explicit link between the classical theory of deformations à la Gerstenhaber (and a fortiori with the Hochschild cohomology) and (weak) PBW-deformations of homogeneous algebras. Our point ...