
TL;DR
This paper characterizes acceptable connected compact Lie groups, showing they must have derived subgroups isomorphic to specific classical groups, and explores invariant functions on certain complex groups.
Contribution
It provides a complete characterization of acceptable connected compact Lie groups based on their derived subgroups and investigates invariant functions on complex orthogonal groups.
Findings
Acceptable groups have derived subgroups isomorphic to specific classical groups.
Invariant functions on $ ext{SO}_4( ext{C})^2$ are not generated by 1-argument invariants.
$ ext{SO}_4( ext{C})$ is acceptable despite complex invariant function properties.
Abstract
In this paper we show that for a connected compact Lie group to be acceptable it is necessary and sufficient that its derived subgroup is isomorphic to a direct product of the groups , , , , . We show that there are invariant functions on which are not generated by 1-argument invariants, though the group is acceptable.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Geometry and complex manifolds · Geometric and Algebraic Topology
