A survey on stability and rigidity results for Lie algebras
Marius Crainic, Florian Schaetz, Ivan Struchiner
TL;DR
This paper reviews and simplifies existing results on the stability and rigidity of Lie algebras, subalgebras, and homomorphisms, and explores conditions for homomorphism stability under automorphisms.
Contribution
It provides unified proofs of known stability and rigidity results and investigates the stability of Lie algebra homomorphisms under all automorphisms.
Findings
Unified proofs of stability and rigidity results
Conditions for homomorphism stability under automorphisms
Enhanced understanding of Lie algebra homomorphism stability
Abstract
We give simple and unified proofs of the known stability and rigidity results for Lie algebras, Lie subalgebras and Lie algebra homomorphisms. Moreover, we investigate when a Lie algebra homomorphism is stable under all automorphisms of the codomain (including outer automorphisms).
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 Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry