GLq(N)-Covariant Quantum Algebras and Covariant Differential Calculus

TL;DR

This paper classifies GLq(N)-covariant quantum algebras with quadratic relations, revealing only two main types, and explores their connection to bicovariant differential calculus on quantum groups.

Contribution

It identifies that only two types of GLq(N)-covariant quantum algebras exist with quadratic relations, linking them to differential calculus on quantum groups.

Findings

Two main types of covariant quantum algebras identified

Connection established with bicovariant differential calculus

Classification up to inessential arbitrariness

Abstract

We consider GLq(N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is disscussed.