English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Using crossed homomorphisms, we show that the category of weakrepresentations (resp. admissible representations) of Lie-Rinehart algebras(resp. Leibniz pairs) is a left module category over the monoidal category ofrepresentations of Lie algebras. In particular, the corresponding bifunctor ofmonoidal categories is established to give new weak representations (resp.admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs).This generalizes and unifies various existing constructions of representationsof many Lie algebras by using this new bifunctor. We construct some crossedhomomorphisms in different situations and use our actions of monoidalcategories to recover some known constructions of representations of variousLie algebras, also to obtain new representations for generalized Witt algebrasand their Lie subalgebras. The cohomology theory of crossed homomorphismsbetween Lie algebras is introduced and used to study linear deformations ofcrossed homomorphisms.

Actions of monoidal categories and representations of Cartan type Lie algebras