The Ring of Invariants for Smooth Completions of Kac-Moody Lie Algebras
Ian Marshall, Tudor Ratiu
TL;DR
This paper proves that the invariant ring of the standard smooth completion of a Kac-Moody Lie algebra is generated by just two elements, simplifying the understanding of its algebraic structure.
Contribution
It establishes that the invariant ring for these completions is generated by the center coefficient and the Killing form, providing a clear description of its generators.
Findings
The invariant ring is generated by the center coefficient and the Killing form.
The structure of the invariant ring is explicitly characterized.
The result simplifies the understanding of invariants in Kac-Moody Lie algebra completions.
Abstract
It is proved that the ring of invariants of the standard smooth completion of a Kac-Moody Lie algebra is functionally generated by two elements: the coefficient of the center and the Killing form.
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
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry