Groebner basis and the Anick resolution for U_K(sl_3^+)

TL;DR

This paper computes the initial steps of a minimal projective resolution for the trivial module over the universal enveloping algebra of the positive part of sl_3, providing insights into its algebraic structure.

Contribution

It introduces a method to explicitly compute the first three steps of a minimal projective resolution for U_K(sl_3^+).

Findings

Computed the first three steps of the resolution.

Provided explicit descriptions of the resolution components.

Enhanced understanding of the algebraic structure of U_K(sl_3^+).

Abstract

We compute three first steps of a minimal projective resolution for the trivial module over U_K(sl_3^+).