Deformation of hom-Lie-Rinehart algebras

Mandal, Ashis Kumar; Mishra, Satyendra Kumar

doi:10.1080/00927872.2019.1698588

Cited by 7 publications

(5 citation statements)

References 20 publications

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“…Remark. If Conditions (10) and ( 11) are not satisfied, then we say that m (without ω) is an ordinary multiderivation (see [MM20] and [EM22]).…”

Section: Restricted Multiderivations and Lie-rinehart Structuresmentioning

confidence: 99%

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On classification and deformations of Lie-Rinehart superalgebras

Ehret¹,

Makhlouf²

2022

Communications in Mathematics

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The purpose of this paper is to study Lie-Rinehart superalgebras over characteristic zero fields, which are consisting of a supercommutative associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in a certain way. We discuss their structure and provide a classification in small dimensions. We describe all possible pairs defining a Lie-Rinehart superalgebra for $\dim(A)\leq 2$ and $\dim(L)\leq 4$. Moreover, we construct a cohomology complex and develop a theory of formal deformations based on formal power series and this cohomology.

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“…Remark. If Conditions (10) and ( 11) are not satisfied, then we say that m (without ω) is an ordinary multiderivation (see [MM20] and [EM22]).…”

Section: Restricted Multiderivations and Lie-rinehart Structuresmentioning

confidence: 99%

“…Remark. If Condition (13) is not satisfied, then there is a one-to-one correspondence between (ordinary) multiderivations m of order 1 satisfying Equation ( 12) and Lie-Rinehart algebras on (A, L) (see [MM20] and [EM22]).…”

Section: Restricted Multiderivations and Lie-rinehart Structuresmentioning

confidence: 99%

On classification and deformations of Lie-Rinehart superalgebras

Ehret¹,

Makhlouf²

2022

Communications in Mathematics

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“…The concept of a Hom-Lie-Rinehart algebra has a geometric analogue which is nowadays called a Hom-Lie algebroid in [2] and [15]. See also [6,[21][22][23]27] for other works on Hom-Lie-Rinehart algebras.…”

Section: Introductionmentioning

confidence: 99%

On split regular Hom-Leibniz-Rinehart algebras

Guo¹,

Zhang²,

Wang³

2020

Preprint

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In this paper, we introduce the notion of the Hom-Leibniz-Rinehart algebra as an algebraic analogue of Hom-Leibniz algebroid, and prove that such an arbitrary split regular Hom-Leibniz-Rinehart algebra L is of the form L = U + γ I γ with U a subspace of a maximal abelian subalgebra H and any I γ , a well described ideal of L, satisfyingIn the sequel, we develop techniques of connections of roots and weights for split Hom-Leibniz-Rinehart algebras respectively. Finally, we study the structures of tight split regular Hom-Leibniz-Rinehart algebras.

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“…In a sequel, they studied formal deformations of Hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations was constructed using multiderivations of Hom-Lie-Rinehart algebras in [15]. Moreover, Zhang et al stuied crossed modules for Hom-Lie-Rinehart algebras in [21], we studied the structures of split regular Hom-Lie Rinehart algebras in [20].…”

Section: Introductionmentioning

confidence: 99%

On 3-Hom-Lie-Rinehart algebras

Guo¹,

Zhang²,

Wang³

2019

Preprint

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We introduce the notion of 3-Hom-Lie-Rinehart algebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we consider extensions of a 3-Hom-Lie-Rinehart algebra and characterize the first cohomology space in terms of the group of automorphisms of an A-split abelian extension and the equivalence classes of A-split abelian extensions. Finally, we study formal deformations of 3-Hom-Lie-Rinehart algebras.

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Deformation of hom-Lie-Rinehart algebras

Abstract: We study formal deformations of hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations is constructed using multiderivations of hom-Lie-Rinehart algebras.

Cited by 7 publications

References 20 publications

On classification and deformations of Lie-Rinehart superalgebras

On classification and deformations of Lie-Rinehart superalgebras

On split regular Hom-Leibniz-Rinehart algebras

On 3-Hom-Lie-Rinehart algebras

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