Generalized $d$-Koszul modules

TL;DR

This paper introduces generalized d-Koszul modules to address an open problem about the structure of odd Ext-modules over d-Koszul algebras, showing they form K-modules over the even Yoneda algebra.

Contribution

The paper defines generalized d-Koszul modules and proves their odd Ext-modules are modules over the even Yoneda algebra, solving a previously open problem.

Findings

Odd Ext-modules of generalized d-Koszul modules are modules over the even Yoneda algebra.

Provides a new framework for understanding Ext-module structures in d-Koszul theory.

Addresses an open problem in the theory of d-Koszul algebras.

Abstract

Generalized \dK modules are introduced to solve an open problem: the odd Ext-module $\Eod(M)$ of a \dK module $M$ over a $d$-Koszul algebra $\m$ is a \K module over the even Yoneda algebra $\Eev(\m)$.