The aim of this paper is to study the structures of split regular Hom-Lie–Rinehart algebras. Let $(L,A)$ be a split regular Hom-Lie–Rinehart algebra. We first show that $L$ is of the form $L=U+\sum _{[\gamma ]\in \Gamma /\thicksim }I_{[\gamma ]}$ with $U$

We introduce the class of split regular BiHom-Poisson superalgebras, which is a natural generalization of split regular Hom-Poisson algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algeb

Let T be a δ-Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of T and present some properties. Also, we study the low-dimensional cohomology and the coboundary operator of T, and then we investigate the deformations and Nijenhuis operators of T by choosing some suitable cohomologies.