Description of bi-quadratic algebras on 3 generators with PBW basis

TL;DR

This paper provides an explicit description of bi-quadratic algebras on three generators that possess a Poincaré-Birkhoff-Witt basis, enhancing understanding of their structure.

Contribution

It offers a detailed classification of bi-quadratic algebras with PBW basis on three generators, which was not previously fully characterized.

Findings

Explicit classification of bi-quadratic algebras with PBW basis

Identification of structural properties of these algebras

Foundation for further algebraic and representation-theoretic studies

Abstract

The aim of the paper is to give an explicit description of bi-quadratic algebras on 3 generators with PBW basis.