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arXiv · 1904.11821

On the structure of split regular Hom-Lie Rinehart algebras

Shengxiang Wang·Xiaohui Zhang·Shuangjian Guo
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Abstract

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 $L=U+\sum_{[γ]\inΓ/\thicksim}I_{[γ]}$ with $U$ a vector space complement in $H$ and $I_{[γ]}$ are well described ideals of $L $ satisfying $I_{[γ]},I_{[δ]}=0$ if $I_{[γ]}\neq I_{[δ]}$. 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.

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Shengxiang Wang, Xiaohui Zhang, Shuangjian Guo. 2019-04-25. On the structure of split regular Hom-Lie Rinehart algebras. https://arxiv.org/abs/1904.11821

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