The group of bi-Galois objects over the coordinate algebra of the Frobenius-Lusztig kernel of SL(2)

TL;DR

This paper constructs an embedding of PSL(n) into the bi-Galois objects over the coordinate algebra of the Frobenius-Lusztig kernel of SL(n), revealing a deep connection between group theory and quantum algebra structures.

Contribution

It introduces a new embedding of PSL(n) into bi-Galois objects over u_q(sl(n))*, establishing an isomorphism for n=2, linking classical groups with quantum algebraic objects.

Findings

Embedding of PSL(n) into bi-Galois objects for odd q

Isomorphism between these structures at n=2

New insights into quantum group symmetries

Abstract

We construct, for q a root of unity of odd order, an embedding of the projective special linear group PSL(n) into the group of bi-Galois objects over u_q(sl(n))*, the coordinate algebra of the Frobenius-Lusztig kernel of SL(n), which is shown to be an isomorphism at n=2.