On the structure of split regular Hom-Lie Rinehart algebras

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 $L=U+{\sum }_{[\gamma ]\in \Gamma /\sim }{I}_{[\gamma ]}$ with $U$ a vector space complement in $H$ and $I_{[\gamma ]}$ are well described ideals of $L$ satisfying $I_{[\gamma ]},I_{[\delta ]}=0$ if $I_{[\gamma ]}\ne I_{[\delta ]}$. 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.

20 pages. arXiv admin note: text overlap with arXiv:1706.07084, arXiv:1504.04236, arXiv:1508.02124 by other authors

References in corpus (1)

• Lie-Rinehart algebras, descent, and quantization

Cited by in corpus (3)

• On split regular Hom-Leibniz-Rinehart algebras
• Hom 3-Lie-Rinehart Algebras
• On 3-Hom-Lie-Rinehart algebras