2023/12/22 by Bjarne Kosmeijer, Hessel Posthuma, Kosmeijer, Bjarne +1
Mathematics · #16E40 #53D17 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2312.14654
openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the Hochschild cohomology of universal enveloping algebras of Lie-Rinehart algebras in terms of the Poisson cohomology of the associated graded quotient algebras. Central in our approach are two cochain complexes of "nonlinear Chevalley-Eilenberg" cochains whose origins lie in Lie-Rinehart modules "up to homotopy", one on the Hochschild cochains of the base algebra, another related to the adjoint representation. The Poincare-Birkhoff-Witt isomorphism is then extended to a certain intertwiner between such modules. Finally, exploiting the twisted Calabi-Yau structure, we obtain results for the dual Hochschild and cyclic homology.