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

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

2003-07-27

arxiv.org/abs/math/0307354v2

Mathematics

K-Theory and Homology

Scientific paper

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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