Lie-Rinehart and Hochschild cohomology for algebras of differential\n operators

2020/06/01 by Francisco Kordon, Kordon, Francisco, Thierry Lambre +1
Mathematics · #16E40 #16S32 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2006.01218

openalex publication_date 2020/06/01 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Let (S,L) be a Lie-Rinehart algebra such that L is S-projective and let\nU be its universal enveloping algebra. In this paper we present a spectral\nsequence which converges to the Hochschild cohomology of U with values on a\nU-bimodule M and whose second page involves the Lie-Rinehart cohomology of\nthe algebra and the Hochschild cohomology of S with values on M. After\ngiving a convenient description of the involved algebraic structures we use the\nspectral sequence to compute explicitly the Hochschild cohomology of the\nalgebra of differential operators tangent to a central arrangement of three\nlines.\n

Related

• The Hochschild cohomology of the enveloping algebra of a Lie-Rinehart\n pair
• Hochschild cohomology of Lie-Rinehart algebras
• Hochschild cohomology of algebras of differential operators tangent to a central arrangement of lines
• The enveloping algebra of a Lie algebra of differential operators
• A Geometric Approach to Hochschild Cohomology of the Exterior Algebra