Left covariant differential calculi on $\widetilde{\rm GL}_q(2)$

TL;DR

This paper develops a ${ m Z}_3$-graded differential calculus framework on the quantum group $ ilde{GL}_q(2)$, extending the concept of quantum de Rham complexes to a ${ m Z}_3$-graded setting.

Contribution

It introduces a novel ${ m Z}_3$-graded differential algebra structure on $ ilde{GL}_q(2)$, constructing left-covariant calculi within this new graded quantum group context.

Findings

Defined ${ m Z}_3$-graded quantum de Rham complex

Constructed left-covariant differential calculi on $ ilde{GL}_q(2)$

Extended quantum group calculus to ${ m Z}_3$-grading

Abstract

In this work, we introduce the ${\mathbb Z}_3$-graded differential algebra, denoted by $\Omega(\widetilde{\rm GL}_q(2))$, treated as the ${\mathbb Z}_3$-graded quantum de Rham complex of ${\mathbb Z}_3$-graded quantum group $\widetilde{\rm GL}_q(2)$. In this sense, we construct left-covariant differential calculi on the ${\mathbb Z}_3$-graded quantum group $\widetilde{\rm GL}_q(2)$.