Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras

DOI10.1016/j.jalgebra.2020.09.017zbMath1464.17008OpenAlexW3088214600WikidataQ115350436 ScholiaQ115350436MaRDI QIDQ2214116

Rong Tang, Shuai Hou, Yun He Sheng

Publication date: 4 December 2020

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2020.09.017

zbMATH Keywords

cohomologydeformation\(L_\infty\)-algebraLie 3-algebra3-Lie algebrarelative Rota-Baxter operator

Mathematics Subject Classification ID

Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Cohomology of Lie (super)algebras (17B56) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Ternary compositions (17A40) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items (12)

Cohomologies and relative Rota-Baxter-Nijenhuis structures of 3-LieRep pairs ⋮ Relative Rota-Baxter operators and symplectic structures on Lie-Yamaguti algebras ⋮ Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and \(\mathcal{O}\)-operators ⋮ The 𝓞N-structure on bimodules over associative conformal algebras ⋮ The cohomology of relative cocycle weighted Reynolds operators and NS-pre-Lie algebras ⋮ Deformations and cohomologies of embedding tensors on 3-Lie algebras ⋮ Cohomologies and deformations of O-operators on Lie triple systems ⋮ Lie \(n\)-algebras and cohomologies of relative Rota-Baxter operators on \(n\)-Lie algebras ⋮ Unnamed Item ⋮ Unnamed Item ⋮ 3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras ⋮ Deformations and cohomology theory of Rota-Baxter 3-Lie algebras of arbitrary weights

Cites Work

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• Simultaneous deformations of algebras and morphisms via derived brackets
• A new cohomology theory associated to deformations of Lie algebra morphisms
• Deformations of coalgebra morphisms.
• Deformation of Leibniz algebra morphisms
• On the Lie-algebraic origin of metric 3-algebras
• The Lie algebra structure of tangent cohomology and deformation theory
• Higher-order simple Lie algebras
• A cohomological perspective on algebraic quantum field theory
• Symplectic, product and complex structures on 3-Lie algebras
• Cohomology and deformations of \(n\)-Lie algebra morphisms
• On Lie \(k\)-algebras
• Deformation-obstruction theory for diagrams of algebras and applications to geometry
• Deformations of associative Rota-Baxter operators
• Lie theory for nilpotent \(L_{\infty}\)-algebras
• Deformations and their controlling cohomologies of \(\mathcal{O}\)-operators
• Commutative algebra cohology and deformations of Lie and associative algebras
• Higher derived brackets and homotopy algebras
• On the deformation of rings and algebras
• Bialgebras, the classical Yang-Baxter equation and Manin triples for 3-Lie algebras
• Leibniz n-algebras
• Nijenhuis Operators on n -Lie Algebras
• Three-algebras and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>6</mml:mn></mml:math>Chern-Simons gauge theories
• On the Deformation of Algebra Morphisms and Diagrams
• Simultaneous deformations and Poisson geometry
• n-ary algebras: a review with applications
• Deformations of 3-algebras
• Differential graded Lie algebras, quasi-hopf algebras and higher homotopy algebras
• What a Classical r-Matrix Really Is
• Generalized Hamiltonian Dynamics
• Splitting of Operations, Manin Products, and Rota–Baxter Operators
• Rota-Baxter 3-Lie algebras

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