Koszul Calculus
Roland Berger, Thierry Lambre, Andrea Solotar
TL;DR
This paper introduces a new calculus tailored for quadratic algebras, incorporating Koszul (co)homology and products, with applications and a proof of Koszul duality for any quadratic algebra.
Contribution
It develops a novel calculus for quadratic algebras, including Koszul (co)homology, cup and cap products, and establishes Koszul duality universally.
Findings
Established Koszul duality for all quadratic algebras.
Developed Koszul (co)homology with cup and cap products.
Provided applications of the calculus.
Abstract
We present a new calculus which is well-adapted to quadratic algebras. This calculus consists in Koszul (co)homology, together with Koszul cup and cap products. Some applications are given. Koszul duality for Koszul (co)homology is proved for any quadratic algebra.
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