We introduce the notion of 3-Hom-Lie-Rinehart algebras and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we consider extensions algebra characterize first space in terms group automorphisms an A-split abelian extension equivalence classes extensions. Finally, study formal deformations algebras.

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, univer...

Kinematic algebras can be realised on geometric spaces and constrain the physical models that live these spaces. Different types of kinematic exist we consider interplay for non-relativistic limits a relativistic system, including both Galilei Carroll limit. We develop framework captures systematically corrections to strict limit by introducing new infinite-dimensional algebras, with emphasis c...

We study an extension of MV algebras, called μMV algebras, in which minimal and maximal fixed points are definable. The first result is that μMV algebras are term-wise equivalent to divisible MV∆algebras, i.e. a combination of two known extensions of MV algebras: divisible MV algebras [4] and MV∆algebras [6]. Using methods from the two known extensions we derive a number of results about μMV al...