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Triple Cohomology of Lie-Rinehart Algebras and the Canonical Class of Associative Algebras

J. M. Casas·M. Ladra·T. Pirashvili
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Abstract

We introduce a bicomplex which computes the triple cohomology of Lie--Rinehart algebras. We prove that the triple cohomology is isomorphic to the Rinehart cohomology \cite{Ri} provided the Lie--Rinehart algebra is projective over the corresponding commutative algebra. As an application we construct a canonical class in the third dimensional cohomology corresponding to an associative algebra.

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J. M. Casas, M. Ladra, T. Pirashvili. 2004-03-05. Triple Cohomology of Lie-Rinehart Algebras and the Canonical Class of Associative Algebras. https://arxiv.org/abs/math/0307354

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