We show that diagonal subalgebras and generalized Veronese subrings of a bigraded Koszul algebra are Koszul. We give upper bounds for the regularity of sidediagonal and relative Veronese modules and apply the results to symmetric algebras and Rees rings.

We record a result concerning the Koszul dual of arity filtration on an operad. This is then used to give conditions under which, for general operad, Poincar\'e/Koszul duality arrow Ayala-Francis equivalence. discuss how little $n$-disks operad $\mathcal{E}_n$ relates their work when combined with self-Koszul $\mathcal{E}_n$.

We provide a uniform vanishing result for the graded components of finite length Koszul module associated to subspace K⊆∧2V as well sharp upper bound its Hilbert function. This purely algebraic statement has interesting applications study number invariants finitely generated groups, such Alexander invariants, Chen ranks, and degree growth virtual nilpotency class. For instance, we explicitly af...

We give a complete picture of the interaction between Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras imposing the condition that standard filtrations of projective modules are...

3 Koszul duality 22 3.1 Quadratic algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Dual coalgebra and algebra . . . . . . . . . . . . . . . . . . . . . 23 3.3 Some more examples . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.1 The free algebra . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.2 An example from Fröberg . . . . . . . . . . . . . . . . . . 28 3.3.3 ...

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 by R. Berger for homogeneous algebras. This notion also extends and generalizes the one recently introduced by the author and A. Rey, which was for the particular case of al...

We define Gerstenhaber’s graded Lie bracket directly on complexes other than the bar complex, under some conditions, resulting in a practical technique for explicit computations. The Koszul complex of a Koszul algebra in particular satisfies our conditions. As examples we recover the Schouten-Nijenhuis bracket for a polynomial ring and the Gerstenhaber bracket for a group algebra of a cyclic gr...

This paper is devoted to graded algebras A having a single homogeneous relation. We give a criterion for A to be N-Koszul where N is the degree of the relation. This criterion uses a theorem due to Gerasimov. As a consequence of the criterion, some new examples of N-Koszul algebras are presented. We give an alternative proof of Gerasimov’s theorem for N = 2, which is related to Dubois-Violette’...