On Dirac Operators and Spectral Geometry of Compact Quantum Groups

TL;DR

This paper explores the construction of Dirac operators and spinors on compact quantum groups, focusing on $SU_q(2)$, comparing different methods, and introducing new examples to advance spectral geometry in quantum group theory.

Contribution

It provides a detailed analysis of Dirac operators on $SU_q(2)$, clarifies relationships between existing approaches, and presents new examples in the spectral geometry of compact quantum groups.

Findings

Analyzed Dirac operators on $SU_q(2)$.

Compared various approaches to constructing Dirac operators.

Introduced new examples in quantum spectral geometry.

Abstract

Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.