On equivariant Dirac operators for $SU_q(2)$

TL;DR

This paper investigates the properties of equivariant Dirac operators on the quantum group SU_q(2), establishing minimality of a known spectral triple and decomposing another in terms of this minimal structure.

Contribution

It introduces the notion of minimality for equivariant spectral triples and applies it to analyze and decompose existing constructions for SU_q(2).

Findings

The spectral triple by Chakraborty and Pal is minimal.

The spectral triple by Dabrowski et al can be decomposed into minimal components.

Abstract

We explain the notion of minimality for an equivariant spectral triple and show that the triple for the quantum SU(2) group constructed by Chakraborty and Pal in \cite{c-p1} is minimal. We also give a decomposition of the spectral triple constructed by Dabrowski {\it et al} \cite{dlssv} in terms of the minimal triple constructed in \cite{c-p1}.