Artinian Gorenstein algebras with linear resolutions

TL;DR

This paper constructs a universal coordinate-free complex for Artinian Gorenstein algebras with linear resolutions, linking algebraic properties to a universal ring and complex.

Contribution

It introduces a universal construction for Artinian Gorenstein algebras with linear resolutions, providing a coordinate-free framework.

Findings

Constructs a ring R and complex G with a universal property.

Links Gorenstein ideals with linear resolutions to a universal algebraic structure.

Provides a coordinate-free approach to studying these algebras.

Abstract

Fix a pair of positive integers d and n. We create a ring R and a complex G of R-modules with the following universal property. Let P be a polynomial ring in d variables over a field and let I be a grade d Gorenstein ideal in P which is generated by homogeneous forms of degree n. If the resolution of P/I by free P-modules is linear, then there exists a ring homomorphism from R to P such that P tensor G is a minimal homogeneous resolution of P/I by free P-modules. Our construction is coordinate free.