Marty reminded us about: A Lie-Rinehart pair (= Lie-Rinehart algebra) (A,L) consists of a commutative associative algebra A and a Lie algebra L with compatible actions of A acts on L and conversely. As for Gerstenhaber algebras, in passing to the homotopy point of view, we have options:

• relax the compatibility up to homotopy

• let A be a commutative A1-agebra

• let L be an Linfty-algebra

• let A be an Ainfty-agebra and L an Linfty-algebra

Of course, once the algebra structure has been relaxed, so too must the compatibility. Which way to go?? Historically, the decision was made by an example occurring in ‘nature’, e.g. in the BFV (Batalin-Fradkin-Vilkovisky) approach to constrained Hamiltonian systems. I hope to present the definition by Lars Kjeseth in his thesis at UNC as well as a more recent version by Luka Vigtagliano.