Graded Lie-Rinehart Algebras

Barreiro, Elisabete; Martín, Antonio; Navarro, R.M.; Sánchez, José M. Peña

doi:10.2139/ssrn.4406095

Cited by 1 publication

(4 citation statements)

References 22 publications

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“…The next result shows that the Λ 1 -connection relation is an equivalence relation (see Proposition 3.2 in [2]).…”

mentioning

confidence: 73%

“…The next result shows that the Σ 1 -connection relation is an equivalence relation. Its proof is analogous to the one for graded Lie triple system in [2], Proposition 3.1.…”

Section: Connections In σ 1 and Decompositionsmentioning

confidence: 84%

“…Our goal in this work is to study the inner structure of arbitrary graded 3-Lie-Rinehart algebras by the developing technique of connections of elements in the supports of the graing of L and A. The finding of the present paper is an improvement and extension of the work on graded Lie-Rinehart algebras in [2].…”

Section: Introductionmentioning

confidence: 84%

“…We will consider the sets Σ ± and Λ ± as in Section 3. Note that, the proof of some results in this section are similar to the one for graded Lie-Rinehard algebra (see [2]), we will omit them. Definition 4.1.…”

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confidence: 95%

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On the structure of graded $3$-Lie-Rinehart algebras

Khalili¹

2023

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We study the structure of a graded 3-Lie-Rinehart algebra L over an associative and commutative graded algebra A. For G an abelian group, we show that if (L, A) is a tight G-graded 3-Lie-Rinehart algebra, then L and A decompose as L = i∈I L i and A = j∈J A j , where any L i is a non-zero graded ideal of L satisfying [L i1 , L i2 , L i3 ] = 0 for any i 1 , i 2 , i 3 ∈ I different from each other, and any A j is a non-zero graded ideal of A satisfying A j A l = 0 for any l, j ∈ J such that j = l, and both decompositions satisfy that for any i ∈ I there exists a unique j ∈ J such that A j L i = 0. Furthermore, any (L i , A j ) is a graded 3-Lie-Rinehart algebra. Also, under certain conditions, it is shown that the above decompositions of L and A are by means of the family of their, respectively, graded simple ideals.

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“…The next result shows that the Λ 1 -connection relation is an equivalence relation (see Proposition 3.2 in [2]).…”

mentioning

confidence: 73%

“…The next result shows that the Σ 1 -connection relation is an equivalence relation. Its proof is analogous to the one for graded Lie triple system in [2], Proposition 3.1.…”

Section: Connections In σ 1 and Decompositionsmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 84%

mentioning

confidence: 95%

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