On the third cohomology of the Lie algebra of vector fields on weighted densities on R

2024/04/28 by Wajd Afsi, Afsi, Wajd, Salem Omri +1
Mathematics · #17B56 #53D55 #58H15 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2406.12872

openalex publication_date 2024/04/28 · openalex created_date 2024/06/22 · openalex updated_date 2026/07/28

Abstract

Let Vect(ℝ) be the Lie algebra of smooth vector fields on ℝ and \mathbbF_λ be the space of λ-densities on ℝ. Vect(ℝ) acts on \mathbbF_λ by Lie derivative. In this paper, we compute the third differential cohomology of the Lie algebra Vect(ℝ) with coeffcients in the space \mathbbF_λ. Explicit cocycles spanning these cohomology spaces are given.

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