RT journal article
T1 Graded Lie-Rinehart algebras
A1 Barreiro, Elisabete
A1 Calderón Martín, Antonio Jesús
A1 Navarro, Rosa M.
A1 Sánchez Delgado, José María
A2 Matemáticas
K1 Lie-Rinehart algebra
K1 Graded algebra
K1 Simple component
K1 Structure theory
AB 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.
PB Elsevier
SN 0393-0440
YR 2023
FD 2023-06-26
LK http://hdl.handle.net/10498/32153
UL http://hdl.handle.net/10498/32153
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 13-nov-2026