A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties

2023/02/15 by Yuly Billig, Billig, Yuly, Colin Ingalls +1 · 1 citation
Mathematics · Physics and Astronomy · #17B66 (Primary) 14F10 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2302.07918

openalex publication_date 2023/02/15 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/28

Abstract

We construct a quasi-coherent sheaf of associative algebras which controls a category of AV-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in étale charts these associative algebras decompose into a tensor product of the algebra of differential operators and the universal enveloping algebra of the Lie algebra of power series vector fields vanishing at the origin.

Cited by

• Differentiable holonomic AV-modules

Related

• Sheaves of AV-modules on quasi-projective varieties
• Algebraic equivarieties over a commutative field
• Category O for the Lie algebra of vector fields on the line
• Representations of Lie algebras of vector fields on affine varieties
• Algebras and varieties