A new $Z_3$-graded quantum group

TL;DR

This paper introduces a novel $Z_3$-graded exterior algebra and constructs a new $Z_3$-graded quantum group, expanding the algebraic framework of quantum groups with grading structures.

Contribution

It presents the first $Z_3$-graded exterior algebra with two generators and develops a corresponding new quantum group, $O( ilde{GL}_q(2))$, with discussion of its properties.

Findings

Defined a $Z_3$-graded exterior algebra with two generators

Constructed a new $Z_3$-graded quantum group $O( ilde{GL}_q(2))$

Analyzed some properties of the new quantum group

Abstract

We introduce a $Z_3$-graded version of exterior (Grassmann) algebra with two generators and using this object we obtain a new $Z_3$-graded quantum group denoted by $O(\widetilde{GL}_q(2))$. We also discuss some properties of ${ O}(\widetilde{GL}_q(2))$.