Higher Braidings of Diagonal Type

TL;DR

This paper extends the concept of Weyl groupoids for Nichols algebras of diagonal type by introducing higher tensor braidings and providing a construction for additional Weyl groupoids, supported by cohomology evidence.

Contribution

It introduces a novel higher tensor braiding framework for Nichols algebras, expanding the structure of Weyl groupoids beyond the diagonal case.

Findings

New construction of Weyl groupoids using higher tensors

Evidence from abelian cohomology for higher braidings

Extension of diagonal braiding concepts to higher tensor structures

Abstract

Heckenberger introduced the Weyl groupoid of a finite-dimensional Nichols algebra of diagonal type. We replace the matrix of its braiding by a higher tensor and present a construction which yields further Weyl groupoids. Abelian cohomology theory gives evidence for the existence of a higher braiding associated to such a tensor.