The nilpotent variety and invariant polynomial functions in the Hamiltonian algebra

2014/01/25 by Junyan Wei, Wei, Junyan
Mathematics · #17B40 #17B50 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B40 #msc:17B50

paper · pdf · doi:10.48550/arxiv.1401.6532

13 pages

arxiv created 2014/01/25 · arxiv updated 2014/01/28

Abstract

Premet has conjectured that the nilpotent variety of any finite-dimensional restricted Lie algebra is an irreducible variety. In this paper, we prove this conjecture in the case of Hamiltonian Lie algebra. and show that its nilpotent variety is normal and a complete intersection. In addition, we generalize the Chevalley Restriction theorem to Hamiltonian Lie algebra. Accordingly, we give the generators of the invariant polynomial ring.

Related

• Nilpotent varieties of some finite dimensional restricted Lie algebras
• General Linear and Symplectic Nilpotent Orbit Varieties
• The invariant polynomials on simple Lie superalgebras
• Invariant theory for the commuting scheme of symplectic Lie algebras
• The structure of Lie algebras with a derivation satisfying a polynomial identity