Weyl equivalence for rank 2 Nichols algebras of diagonal type

TL;DR

This paper investigates Weyl equivalence relations among rank 2 Nichols algebras of diagonal type, explicitly determining these relations for modules with finite Gel'fand--Kirillov dimension, contributing to the classification of such algebras.

Contribution

It explicitly characterizes Weyl equivalence for all rank 2 diagonal Nichols algebras with finite Gel'fand--Kirillov dimension, advancing understanding of their structure.

Findings

Explicit determination of Weyl equivalence relations for rank 2 Nichols algebras

Identification of conditions preserving dimension and Gel'fand--Kirillov dimension

Contribution to classification of diagonal Nichols algebras

Abstract

Yetter--Drinfel'd modules of diagonal type admit an equivalence relation which conjecturally preserves dimension and Gel'fand--Kirillov dimension of the corresponding Nichols algebras. This relation is determined explicitly for all rank 2 Yetter--Drinfeld modules where the Gel'fand--Kirillov dimension is known to be finite. Key Words: Brandt groupoid, Hopf algebra, pseudo-reflections, Weyl group