ACTIONS OF MONOIDAL CATEGORIES AND REPRESENTATIONS OF CARTAN TYPE LIE ALGEBRAS

Abstract Using crossed homomorphisms, we show that the category of weak representations (respectively admissible representations) Lie–Rinehart algebras Leibniz pairs) is a left module over monoidal Lie algebras. In particular, corresponding bifunctor categories established to give new pairs). This generalises and unifies various existing constructions many by using this bifunctor. We construct some homomorphisms in different situations use our actions recover known obtain for generalised Witt their subalgebras. The cohomology theory between introduced used study linear deformations homomorphisms.