Algebras of Quotients of Jordan–Lie Algebras

Guo, Wei; Chen, Liangyun

doi:10.1080/00927872.2015.1087009

Cited by 6 publications

(2 citation statements)

References 5 publications

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“…In [6], García and Gómez defined Martindalelike quotients for Lie triple systems with respect to power filters of sturdy ideals and constructed the maximal system of quotients in the nondegenerate cases. More research about quotients of Lie systems refer in references [8,10]. In [11], Martínez derived a necessary and sufficient Ore type condition for a Jordan algebra to have a ring of fractions, which is the origin of algebras of quotients of Jordan systems.…”

Section: Introductionmentioning

confidence: 99%

Algebras of quotients of Hom-Lie algebras

Yao,

Chen

2020

Preprint

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In this paper, we introduce the notion of algebras of quotients of Hom-Lie algebras and investigate some properties which can be lifted from a Hom-Lie algebra to its algebra of quotients. We also give some necessary and sufficient conditions for Hom-Lie algebras having algebras of quotients. We also examine the relationship between a Hom-Lie algebra and the associative algebra generated by inner derivations of the corresponding Hom-Lie algebra of quotients. Moreover, we introduce the notion of dense extensions and get a proposition about Hom-Lie algebras of quotients via dense extensions.

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Section: Introductionmentioning

confidence: 99%

Algebras of quotients of Hom-Lie algebras

Yao,

Chen

2020

Preprint

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“…In [12], García and Gómez defined Martindale-like quotients for Lie triple systems with respect to power filters of sturdy ideals and constructed the maximal system of quotients in the nondegenerate cases. More research about quotients of Lie systems refer in references [14,19]. In [17], Martínez derived a necessary and sufficient Ore type condition for a Jordan algebra to have a ring of fractions, which is the origin of algebras of quotients of Jordan systems.…”

Section: Introductionmentioning

confidence: 99%

Algebras of quotients and Martindale-like quotients of Leibniz algebras

Yao¹,

Ma²,

Tang³

et al. 2020

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In this paper, the definitions of algebras of quotients and Martandale-like qoutients of Leibniz algebras are introduced and the interactions between the two quotients are determined. Firstly, some important properties which not only hold for a Leibniz algebras but also can been lifted to its algebras of quotients are investigated. Secondly, for any semiprime Leibniz algebra, its maximal algebra of quotients is constucted and a Passman-like characterization of the maximal algebra is described. Thirdly, the relationship between a Leibniz algebra and the associative algebra which is generated by left and right multiplication operators of the corresponding Leibniz algebras of quotients are examined. Finally, the definition of dense extensions and some vital properties about Leibnia algebras via dense extensions are introduced.

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δ-Hom-Jordan Lie superalgebras

Chen

Zhao

2017

Communications in Algebra

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Algebras of Quotients of Jordan–Lie Algebras

Cited by 6 publications

References 5 publications

Algebras of quotients of Hom-Lie algebras

Algebras of quotients of Hom-Lie algebras

Algebras of quotients and Martindale-like quotients of Leibniz algebras

δ-Hom-Jordan Lie superalgebras

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