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