In this talk I will introduce a cup-cap duality in the Koszul calculus of N-homogeneous algebras. As an application of this duality, it follows that the graded symmetry of the Koszul cap product is a consequence of the graded commutativity of the Koszul cup product. I will also comment on a conceptual approach to this problem that may lead to a proof of the graded commutativity, based on derived categories in the framework of DG-algebras and DG-bimodules.
This is joint work with Roland Berger, and based on this arXiv paper.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
