Graded Lie-Rinehart algebras

The present work introduces the class of graded Lie-Rinehart algebras as a natural generalization Lie algebras. It is demonstrated that tight G-graded algebra L over commutative and associative A, where G an abelian group, can be decomposed into orthogonal direct sums L=⨁i∈IIi A=⨁j∈JAj, each Ii Aj non-zero ideal respectively. Additionally, both decompositions satisfy for any i∈I, there exists unique j∈J such AjIi≠0 Aj. In case maximal length, aforementioned A are through inde- composable (graded) ideals, simplicity also characterized.