Abstract
The problem of the representation of an action of a Lie–Rinehart algebra on a Lie 𝖠-algebra by means of a homomorphism of Lie–Rinehart algebras is studied. An eight-term exact sequence associated to an epimorphism of Lie–Rinehart algebras for the cohomology of Lie–Rinehart algebras developed by Casas, Ladra and Pirashvili is obtained. This sequence is applied to study the obstruction theory of Lie–Rinehart algebra extensions.
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