On the structure of split regular Hom-Lie Rinehart algebras

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 $L=U+sum_{[gamma]inGamma/thicksim}I_{[gamma]}$ with $U$ a vector space complement in $H$ and $I_{[gamma]}$ are well described ideals of $L $ satisfying $I_{[gamma]},I_{[delta]}=0$ if $I_{[gamma]} eq I_{[delta]}$. Also, we discuss the weight spaces and decompositions of $A$ and present the relation between the decompositions of $L$ and $A$. Finally, we consider the structures of tight split regular Hom-Lie Rinehart algebras.