Representations of Lie algebras of vector fields on affine varieties

Yuly Billig; Vyacheslav Futorny; Jonathan Nilsson

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arXiv · 1709.08863

Representations of Lie algebras of vector fields on affine varieties

Yuly Billig·Vyacheslav Futorny·Jonathan Nilsson

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Abstract

For an irreducible affine variety $X$ over an algebraically closed field of characteristic zero we define two new classes of modules over the Lie algebra of vector fields on $X$ - 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.

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BibTeX RIS

Yuly Billig, Vyacheslav Futorny, Jonathan Nilsson. 2017-09-26. Representations of Lie algebras of vector fields on affine varieties. https://arxiv.org/abs/1709.08863

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