73 citations · 133 across the 13 of their papers we have counts for
15 papers
Calabi-Yau property in derived Koszul calculus
Roland Berger, Jun Maillard
A Poincaré Van den Bergh duality theorem for strong Kc-Calabi-Yau algebras was obtained by R. Taillefer and the first author under the assumption that the derived functors of funct…
A cup-cap duality in Koszul calculus
Roland Berger, Andrea Solotar
We introduce a cup-cap duality in the Koszul calculus of N-homogeneous algebras. As an application, we prove that the graded symmetry of the Koszul cap product is a consequence of…
Koszul calculus of preprojective algebras
Roland Berger, Rachel Taillefer
We show that the Koszul calculus of a preprojective algebra, whose graph is distinct from A and A, vanishes in any (co)homological degree . Moreover, its (higher) co…
N-Cartan calculus
Roland Berger
We examine the N-Koszul calculus for the N-symmetric algebras. The case N=2 corresponds to the Elie Cartan calculus. We conjecture that, as in the case N=2, the N-Cartan calculus e…
Koszul calculus for N-homogeneous algebras
Roland Berger
We extend the Koszul calculus defined on quadratic algebras by Berger, Lambre and Solotar, to N-homogeneous algebras. When N>2, the Koszul cup and cap products are defined by speci…
A criterion for homogeneous potentials to be 3-Calabi-Yau
Roland Berger, Andrea Solotar
We give a necessary and sufficient condition for an N-Koszul algebra defined by a homogeneous potential, to be 3-Calabi-Yau. As an application, we recover two families of 3-Calabi-…