Deformations of associative Rota-Baxter operators

DOI10.1016/j.jalgebra.2020.05.016zbMath1458.16008arXiv1909.08320OpenAlexW3031198813MaRDI QIDQ2193197

Apurba Das

Publication date: 25 August 2020

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

Full work available at URL: https://arxiv.org/abs/1909.08320

zbMATH Keywords

Hochschild cohomologyformal deformationRota-Baxter operator\(\mathcal{O}\)-operatorassociative \(r\)-matrix

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Deformations of associative rings (16S80) Associative rings and algebras with additional structure (16W99)

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The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators, Cohomology and deformations of weighted Rota–Baxter operators, Representations and cohomologies of relative Rota-Baxter Lie algebras and applications, Cohomology and deformations of crossed homomorphisms, Cohomology and deformations of \(\mathcal{O}\)-operators on Hom-associative algebras, Cohomology and deformations of twisted Rota-Baxter operators and NS-algebras, Cohomology and deformations of dendriform algebras, and Dend_∞-algebras, Deformations and cohomologies of relative Rota-Baxter operators on Lie algebroids and Koszul-Vinberg structures, \(\mathcal{O}\)-operators and Nijenhuis operators of associative conformal algebras, The 𝓞N-structure on bimodules over associative conformal algebras, A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras, The cohomology of relative cocycle weighted Reynolds operators and NS-pre-Lie algebras, Rota–Baxter family Ω-associative conformal algebras and their cohomology theory, Bimodules over relative Rota-Baxter algebras and cohomologies, Relative Rota–Baxter Leibniz algebras, their characterization and cohomology, Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects, Cohomologies of Rota-Baxter Lie triple systems and applications, L ∞ -structures and cohomology theory of compatible O-operators and compatible dendriform algebras, Cohomologies and deformations of O-operators on Lie triple systems, Cohomologies of relative Rota-Baxter Lie algebras with derivations and applications, Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases, Crossed modules and non-abelian extensions of Rota-Baxter Leibniz algebras, Compatible structures of nonsymmetric operads, Manin products and Koszul duality, Nonabelian embedding tensors, Lie theory and cohomology of relative Rota–Baxter operators, Cohomology and deformations of generalized Reynolds operators on Leibniz algebras, Lie \(n\)-algebras and cohomologies of relative Rota-Baxter operators on \(n\)-Lie algebras, Unnamed Item, Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras, Twisted Rota–Baxter operators and Reynolds operators on Lie algebras and NS-Lie algebras, Involutive and oriented dendriform algebras, Twisted Rota-Baxter families and NS-family algebras, Deformations, cohomologies and integrations of relative difference Lie algebras, 3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras

Cites Work

• Unnamed Item
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• Averaging operators on \(C_ \infty (X)\)
• On the existence of deformations of complex analytic structures
• An analytic problem whose solution follows from a simple algebraic identity
• On the representation of averaging operators
• Averaging algebras, Schröder numbers, rooted trees and operads
• Twisting on associative algebras and Rota-Baxter type operators.
• Quantum analogy of Poisson geometry, related dendriform algebras and Rota-Baxter operators
• Cohomologies and deformations of right-symmetric algebras
• Deformation quantization of Poisson manifolds
• Double constructions of Frobenius algebras, Connes cocycles and their duality
• Baxter algebras and shuffle products
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Compatible \(\mathcal{O}\)-operators on bimodules over associative algebras
• On deformations of complex analytic structures. II
• The cohomology structure of an associative ring
• Deformations and their controlling cohomologies of \(\mathcal{O}\)-operators
• Rota-Baxter algebras and dendriform algebras.
• On the structure of free Baxter algebras
• Higher derived brackets and homotopy algebras
• On the deformation of rings and algebras
• On the cohomology groups of an associative algebra
• A THEOREM ON STABILITY OF COMPLEX STRUCTURES
• Calculus on Poisson Manifolds
• Baxter algebras and combinatorial identities. II
• QUANTUM BI-HAMILTONIAN SYSTEMS
• Dirac Manifolds
• Nijenhuis operators on pre-Lie algebras
• Cohomology and deformations in graded Lie algebras
• Pre-Poisson algebras
• On the associative analog of Lie bialgebras
• Derived bracket construction and Manin products