On 3-Lie algebras with a derivation

Guo, Shuangjian; Saha, Ripan

doi:10.1007/s13370-022-00998-7

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…There is an enormous literature on this subject, including differential Galois theory, see [14]. In recent times, there is a numerous studies on different type of algebras with derivations, see [3], [7], [19]. Similarly, degenerations of algebras is an interesting subject, which were studied in various papers, for the study of degenerations of Leibniz algebras and related structures, see [11], [8], [10].…”

Section: Introductionmentioning

confidence: 99%

Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras

Mondal¹,

Saha²

2023

Communications in Mathematics

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A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. We define representation and dual representation of Rota-Baxter Leibniz algebras. Next, we define a cohomology theory of Rota-Baxter Leibniz algebras. We also study the infinitesimal and formal deformation theory of Rota-Baxter Leibniz algebras and show that our cohomology is deformation cohomology. Moreover, We define an abelian extension of Rota-Baxter Leibniz algebras and show that equivalence classes of such extensions are related to the cohomology groups.

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Section: Introductionmentioning

confidence: 99%

Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras

Mondal¹,

Saha²

2023

Communications in Mathematics

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“…In [23], Tang et al investigated the deformation and extension of Lie algebras with derivations from the cohomological point of view. The results of [23] have been extended to 3-Lie algebras with derivations [24,25]. More research on algebraic structures with derivations has been developed; see [26][27][28][29][30][31] and references cited therein.…”

Section: Introductionmentioning

confidence: 99%