On the structure of split regularHom-Lie–Rinehart algebras
Tom 160 / 2020
Streszczenie
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 $U$ a vector space complement of $\sum _{\gamma \in \Gamma ,-\gamma \in \Lambda }A_{-\gamma }L_{\gamma }+\sum _{\gamma \in \Gamma }[L_{-\gamma },L_{\gamma }]$ in $H$ and with each $I_{[\gamma ]}$ being a well defined ideal of $L,$ satisfying $[I_{[\gamma ]},I_{[\delta ]}]=0$ if $I_{[\gamma ]}\neq I_{[\delta ]}$. 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.
