Double loop quantum enveloping algebras

TL;DR

This paper explores the homological properties and representations of a two-parameter quantum enveloping algebra of sl(2), expanding understanding of its algebraic structure and potential applications.

Contribution

It introduces and analyzes the homological aspects and representations of the new two-parameter quantum algebra U_{g,h} of sl(2).

Findings

Characterizes homological properties of U_{g,h}.

Describes the representation theory of the algebra.

Provides new insights into two-parameter quantum groups.

Abstract

In this paper we describe certain homological properties and representations of a two-parameter quantum enveloping algebra $U_{g,h}$ of ${\frak {sl}}(2)$, where $g,h$ are group-like elements.