Compact Lie groups and complex reductive groups

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category of topological spaces are equivalent. This can also be interpreted as an equivalence of infinity categories.

Keywords

compact Lie group, reductive group, Tannaka formalism, infinity category

2010 Mathematics Subject Classification

Primary 18D20. Secondary 22E46.

The full text of this article is unavailable through your IP address: 3.137.219.213

Received 20 April 2022

Received revised 6 April 2023

Accepted 25 April 2023

Published 20 March 2024