Higher Koszul duality for associative algebras

TL;DR

This paper develops a comprehensive framework for higher Koszul duality in N-homogeneous algebras, introducing new algebraic structures and a universal description of Koszul duals, with implications for algebraic operations and syzygies.

Contribution

It introduces a unifying approach to higher Koszul duality, including a new algebraic structure and Gr"obner bases for non-symmetric operad algebras.

Findings

Universal description of Koszul dual algebra

Introduction of Gr"obner bases for non-symmetric operads

Framework unifies key concepts in higher Koszul duality

Abstract

We present a unifying framework for the key concepts and results of higher Koszul duality theory for N-homogeneous algebras: the Koszul complex, the candidate for the space of syzygies, and the higher operations on the Yoneda algebra. We give a universal description of the Koszul dual algebra under a new algebraic structure. For that we introduce a general notion: Gr\"obner bases for algebras over non-symmetric operads.