On Anick resolution: from the original setting to the language of non-commutative Groebner bases

TL;DR

This paper bridges Anick's original resolution with the framework of non-commutative Groebner bases, providing a comprehensive dictionary to connect different approaches in algebraic resolutions.

Contribution

It translates Anick's resolution into the language of non-commutative Groebner bases, facilitating understanding and application across different algebraic frameworks.

Findings

Established a correspondence between Anick's resolution and Groebner bases

Provided a unified terminology for different approaches

Enhanced accessibility of Anick's resolution techniques

Abstract

Anick introduced a resolution, that now bears his name, of a field using an augmented algebra over that field. We present here what one could call a dictionary between Anick's original paper and the other resources on the matter, most of which use the language of non-commutative Groebner bases.