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Representations of Lie algebras of vector fields on affine varieties

Journal article
Authors Y. Billig
V. Futorny
Jonathan Nilsson
Published in Israel Journal of Mathematics
ISSN 0021-2172
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Subject categories Algebra and Logic


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 [23]. We prove general simplicity theorems for these two types of modules and establish a pairing between them. © 2019, The Hebrew University of Jerusalem.

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