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https://hdl.handle.net/10316/111998
Title: | Graded Lie-Rinehart algebras | Authors: | Barreiro, Elisabete Calderón, Antonio J. Navarro, Rosa M. Sánchez, José M. |
Keywords: | Lie-Rinehart algebra; Graded algebra; Simple component; Structure theory | Issue Date: | 25-Feb-2022 | Publisher: | Elsevier | Serial title, monograph or event: | Journal of Geometry and Physics | Volume: | 191 | Abstract: | We introduce the class of graded Lie-Rinehart algebras as a natural generalization of the one of graded Lie algebras. For $G$ an abelian group, we show that if $L$ is a tight $G$-graded Lie-Rinehart algebra over an associative and commutative $G$-graded algebra $A$ then $L$ and $A$ decompose as the orthogonal direct sums $L = \bigoplus_{i \in I}I_i$ and $A = \bigoplus_{j \in J}A_j$, where any $I_i$ is a non-zero ideal of $L$, any $A_j$ is a non-zero ideal of $A$, and both decompositions satisfy that for any $i \in I$ there exists a unique $j \in J$ such that $A_jI_i \neq 0$. Furthermore, any $I_i$ is a graded Lie-Rinehart algebra over $A_j$. Also, under mild conditions, it is shown that the above decompositions of $L$ and $A$ are by means of the family of their, respective, gr-simple ideals. | Description: | arXiv admin note: substantial text overlap with arXiv:1706.07084 | URI: | https://hdl.handle.net/10316/111998 | ISSN: | 03930440 | DOI: | 10.1016/j.geomphys.2023.104914 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais I&D CMUC - Artigos em Revistas Internacionais |
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