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Lie-Rinehart algebras ≃ acyclic Lie ∞-algebroids.
- 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