Graded Lie-Rinehart algebras
Identificadores
URI: http://hdl.handle.net/10498/32153
DOI: 10.1016/j.geomphys.2023.104914
ISSN: 0393-0440
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2023-06-26Department
MatemáticasSource
Journal of Geometry and Physics, Vol. 191, 2023Abstract
The present work introduces the class of graded Lie-Rinehart algebras as a natural generalization of graded Lie algebras. It is demonstrated that a tight G-graded Lie-Rinehart algebra Lover a commutative and associative G-graded algebra A, where G is an abelian group, can be decomposed into the orthogonal direct sums L = i∈I Ii and A = j∈J Aj, where each Ii and Aj is a non-zero ideal of L and A, respectively. Additionally, both decompositions satisfy that for any i ∈I, there exists a unique j ∈ J such that AjIi=0 and that any Ii is a graded Lie-Rinehart algebra over Aj. In the case of maximal length, the aforementioned decompositions of L and Aare through indecomposable (graded) ideals, and the (graded) simplicity of any Ii and any Aj are also characterized.
Subjects
Lie-Rinehart algebra; Graded algebra; Simple component; Structure theoryCollections
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