A cup-cap duality in Koszul calculus
Representation Theory
2022-06-03 v2 Rings and Algebras
Abstract
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 the graded commutativity of the Koszul cup product. We propose a conceptual approach that may lead to a proof of the graded commutativity, based on derived categories in the framework of DG algebras and DG bimodules. Various enriched structures are developed in a weaker situation corresponding to N>2.
Cite
@article{arxiv.2007.00627,
title = {A cup-cap duality in Koszul calculus},
author = {Roland Berger and Andrea Solotar},
journal= {arXiv preprint arXiv:2007.00627},
year = {2022}
}
Comments
30 pages, a few minor changes