Anyonic FRT construction

TL;DR

This paper extends the Faddeev-Reshetikhin-Takhtajan method to construct matrix bialgebras in the anyonic or rac{Z}{n}-graded case, resulting in braided groups with phase-factor braiding.

Contribution

It introduces a novel extension of the FRT construction to anyonic and rac{Z}{n}-graded settings, creating new braided quantum groups.

Findings

Constructed anyonic quantum matrices as braided groups.

Extended FRT method to rac{Z}{n}-graded cases.

Demonstrated phase-factor braiding in the resulting structures.

Abstract

The Faddeev-Reshetikhin-Takhtajan method to construct matrix bialgebras from non-singular solutions of the quantum Yang-Baxter equation is extended to the anyonic or $\Z_n$-graded case. The resulting anyonic quantum matrices are braided groups in which the braiding is given by a phase factor.