Representations of Lie algebras of vector fields on affine varieties
| Autor: | Vyacheslav Futorny, Jonathan Nilsson, Yuly Billig |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
ÁLGEBRAS DE LIE General Mathematics Polynomial ring 17B20 17B66 (Primary) 13N15 (Secondary) 010102 general mathematics 0102 computer and information sciences 01 natural sciences 010201 computation theory & mathematics Tensor (intrinsic definition) Lie algebra FOS: Mathematics Vector field Gauge theory Affine transformation Representation Theory (math.RT) 0101 mathematics Algebraically closed field Affine variety Mathematics - Representation Theory Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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