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 $U$

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.

We mainly construct a bicrossproduct for a finite-dimensional monoidal Hom-Hopf algebra $(H,\alpha )$, generalizing Majid’s bicrossproduct. Naturally, the Hom-type bicrossproduct leads to the Drinfel’d double $(H^{\rm op}\bowtie H^{\ast },\alpha \otimes (