Gr\"obner--Shirshov bases for Vinberg--Koszul--Gerstenhaber right-symmetric algebras

TL;DR

This paper develops a Composition-Diamond lemma for right-symmetric algebras and constructs a Gr"obner-Shirshov basis for their universal enveloping algebras of Lie algebras, advancing algebraic computational methods.

Contribution

It introduces a Composition-Diamond lemma specific to right-symmetric algebras and applies it to find Gr"obner-Shirshov bases for their universal enveloping algebras.

Findings

Established the Composition-Diamond lemma for right-symmetric algebras

Constructed Gr"obner-Shirshov basis for universal enveloping right-symmetric algebra

Enhanced algebraic computational techniques for these structures

Abstract

In this paper, we establish the Composition-Diamond lemma for right-symmetric algebras. As an application, we give a Gr\"{o}bner-Shirshov basis for universal enveloping right--symmetric algebra of a Lie algebra.