Representations of Lie algebras of vector fields on affine varieties
Artikel i vetenskaplig tidskrift, 2019

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.

Författare

Yuly Billig

Carleton University

Vyacheslav Futorny

Universidade de Sao Paulo (USP)

Jonathan Nilsson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Israel Journal of Mathematics

0021-2172 (ISSN) 15658511 (eISSN)

Vol. 233 1 379-399

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

Fundament

Grundläggande vetenskaper

DOI

10.1007/s11856-019-1909-z

Mer information

Senast uppdaterat

2019-12-02