On the structure of spaces of commuting elements in compact Lie groups

TL;DR

This paper investigates the topological properties of spaces of homomorphisms from finitely generated abelian groups into products of classical compact Lie groups, revealing their structural invariants.

Contribution

It provides new insights into the topological invariants of Hom(rac,) spaces for classical Lie groups, expanding understanding of their structure.

Findings

Identification of topological invariants of Hom(rac,) spaces

Analysis of the structure of commuting elements in classical Lie groups

Extension of known results to product groups

Abstract

In this note we study topological invariants of the spaces of homomorphisms Hom(\pi,G), where \pi\ is a finitely generated abelian group and G is a compact Lie group arising as an arbitrary finite product of the classical groups SU(r), U(q) and Sp(k).