On quasitriangular structures in Hopf algebras arising from exact group factorizations

TL;DR

This paper proves that certain Hopf algebras derived from exact factorizations of almost simple finite groups do not admit quasitriangular structures, highlighting limitations in their algebraic properties.

Contribution

It establishes the non-existence of quasitriangular structures in bicrossed product Hopf algebras from exact factorizations of almost simple finite groups.

Findings

Bicrossed product Hopf algebras from exact factorizations in almost simple groups lack quasitriangular structures.

The result applies specifically to simple and symmetric groups.

This advances understanding of the algebraic properties of Hopf algebras related to group factorizations.

Abstract

We show that bicrossed product Hopf algebras arising from exact factorizations in almost simple finite groups, so in particular, in simple and symmetric groups, admit no quasitriangular structure.