Contact Lie algebras, generic stabilisers, and affine seaweeds
Abstract
Let q = Lie Q be an algebraic Lie algebra of index 1, i.e., a generic Q -orbit on q ⁎ ⁎ has codimension 1. We show that the following conditions are equivalent: q is contact; a generic Q -orbit on q ⁎ ⁎ is not conical; there is a generic stabiliser for the coadjoint action of q . In addition, if q is contact, then the subalgebra S ( q ) si ⊂ S ( q ) generated by symmetric semi-invariants of q is a polynomial ring. We study also affine seaweed Lie algebras of type A and find some contact as well as non-contact examples among them.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Journal of Algebra
- Volume
- 692
- Pages
- 401–421
- Publication date
- 2 January 2026
- Language
- EN