The spectral space of conjugacy classes of subgroups of a compact Lie group

2025/09/23 by Greenlees, J. P. C.
#22E99 #55P42 #55P91 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2509.19409

Abstract

The space of conjugacy classes of subgroups of a compact Lie groups with its Zariski topology splits as a disjoint union of clopen blocks, each dominated by a subgroup H with finite Weyl group, and the structure of each block is controlled by an integral representation of the component group of H

Citations

• An algebraic model for rational U(2)-spectra
• Rational G-spectra for rank 2 toral groups of mixed type
• Algebraic models for 1-dimensional categories of rational G-spectra
• Spaces of subgroups of toral groups
• Prismatic decompositions and rational G-spectra
• The Balmer spectrum of rational equivariant cohomology theories
• HZ-algebra spectra are differential graded algebras

Related

• A note on closed subgroups of compact Lie groups
• Spaces of subgroups of toral groups
• Topological properties of Ad-semisimple conjugacy classes in Lie groups
• Centralizers of Commuting Elements in Compact Lie Groups
• On the structure of spaces of commuting elements in compact Lie groups