English

Compact Lie Groups and Complex Reductive Groups

Representation Theory 2023-04-27 v3 Category Theory Group Theory

Abstract

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

Cite

@article{arxiv.2109.13702,
  title  = {Compact Lie Groups and Complex Reductive Groups},
  author = {John Jones and Dmitriy Rumynin and Adam Thomas},
  journal= {arXiv preprint arXiv:2109.13702},
  year   = {2023}
}

Comments

11 pages. Version 2: minor edits. Version 3: the final journal version with minor edits