Back to Search Start Over

Lie-Rinehart algebras ≃ acyclic Lie ∞-algebroids.

Authors :
Laurent-Gengoux, Camille
Louis, Ruben
Source :
Journal of Algebra. Mar2022, Vol. 594, p1-53. 53p.
Publication Year :
2022

Abstract

We show that there is an equivalence of categories between Lie-Rinehart algebras over a commutative algebra O and homotopy equivalence classes of negatively graded Lie ∞-algebroids over their resolutions (=acyclic Lie ∞-algebroids). This extends to a purely algebraic setting the construction of the universal Q -manifold of a locally real analytic singular foliation of [26,28]. In particular, it makes sense for the universal Lie ∞-algebroid of every singular foliation, without any additional assumption, and for Androulidakis-Zambon singular Lie algebroids. Also, to any ideal I ⊂ O preserved by the anchor map of a Lie-Rinehart algebra A , we associate a homotopy equivalence class of negatively graded Lie ∞-algebroids over complexes computing Tor O (A , O / I). Several explicit examples are given. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00218693
Volume :
594
Database :
Academic Search Index
Journal :
Journal of Algebra
Publication Type :
Academic Journal
Accession number :
154438075
Full Text :
https://doi.org/10.1016/j.jalgebra.2021.11.023