Representations of Lie algebras of vector fields on affine varieties
Representation Theory
2017-09-27 v1
Abstract
For an irreducible affine variety over an algebraically closed field of characteristic zero we define two new classes of modules over the Lie algebra of vector fields on - gauge modules and Rudakov modules, which admit a compatible action of the algebra of functions. Gauge modules are generalizations of modules of tensor densities whose construction was inspired by non-abelian gauge theory. Rudakov modules are generalizations of a family of induced modules over the Lie algebra of derivations of a polynomial ring studied by Rudakov. We prove general simplicity theorems for these two types of modules and establish a pairing between them.
Keywords
Cite
@article{arxiv.1709.08863,
title = {Representations of Lie algebras of vector fields on affine varieties},
author = {Yuly Billig and Vyacheslav Futorny and Jonathan Nilsson},
journal= {arXiv preprint arXiv:1709.08863},
year = {2017}
}