Triple cohomology of Lie-Rinehart algebras and the canonical class of associative algebras

摘要

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 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 in associative algebra and extend Sridharan's result on almost commutitive algebras. (c) 2005 Elsevier Inc. All rights reserved.