Rigidity of Graded Regular Algebras
E. Kirkman (1), J. Kuzmanovich (1), J. J. Zhang (2) ((1) Wake Forest, University, (2) University of Washington)
TL;DR
This paper proves that certain graded regular algebras, including universal enveloping algebras and Weyl algebras, are rigid under finite group actions, extending previous rigidity results to a graded setting.
Contribution
It establishes a graded version of the rigidity theorem for universal enveloping algebras, Weyl algebras, and Sklyanin algebras, showing they cannot be isomorphic to their fixed subrings under finite group actions.
Findings
Homogenization of universal enveloping algebra is rigid.
Rees rings of Weyl algebras are rigid.
Sklyanin algebras also exhibit rigidity.
Abstract
We prove a graded version of Alev-Polo's rigidity theorem: the homogenization of the universal enveloping algebra of a semisimple Lie algebra and the Rees ring of the Weyl algebras cannot be isomorphic to their fixed subring under any finite group action. We also show the same result for other classes of graded regular algebras including the Sklyanin algebras.
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 · Homotopy and Cohomology in Algebraic Topology