Second cohomology of <i>q</i>-deformed Witt superalgebras

Ammar, Faouzi; Makhlouf, Abdenacer; Saadaoui, Nejib

doi:10.1063/1.4807717

Cited by 6 publications

(2 citation statements)

References 33 publications

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“…The Hom-Lie superalgebras were introduced in [3], and as an illustration, the q-deformed Witt superalgebra was constructed. The cohomology theory of Hom-Lie superalgebras was introduced and, as an application, the second cohomology of the q-deformed Witt superalgebra was computed in [4,5]. The notion of a Hom-Lie color algebra was introduced and studied in [30].…”

Section: Introductionmentioning

confidence: 99%

Biderivations of Hom-Lie algebras and superalgebras

Yuan¹,

Li²

2021

Preprint

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In this paper, we introduce the notions of biderivations and linear commuting maps of Hom-Lie algebras and superalgebras. Then we compute biderivations of the q-deformed W (2, 2) algebra, q-deformed Witt algebra and superalgebras by elementary and direct calculations. As an application, linear commuting maps on these algebras are characterized. Also, we introduce the notions of α-derivations and α-biderivations for Hom-Lie algebras and superalgebras, and we establish a close relation between α-derivations and α-biderivations. As an illustration, we prove that the q-deformed W (2, 2)-algebra, the q-deformed Witt algebra and superalgebra have no nontrivial α-biderivations. Finally, we present an example of Hom-Lie superalgebras with nontrivial α-super-derivations and biderivations.

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Section: Introductionmentioning

confidence: 99%

Biderivations of Hom-Lie algebras and superalgebras

Yuan¹,

Li²

2021

Preprint

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“…The q-deformed Witt superalgebra W q was defined in [1] as a main example of Hom-Lie superalgebras. The cohomology and deformations of W q were studied in [2,3]. The first and second cohomology groups of the q-deformed Heisenberg-Virasoro algebra of Hom-type are computed in [5].…”

Section: Introductionmentioning

confidence: 99%