Integration and geometrization of Rota-Baxter Lie algebras

DOI10.1016/j.aim.2021.107834zbMath1468.17026arXiv2009.03492OpenAlexW3083804758MaRDI QIDQ2037611

Honglei Lang, Li Guo, Yun He Sheng

Publication date: 8 July 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.03492

zbMATH Keywords

integrationpost-Lie algebroidRota-Baxter Lie algebroidRota-Baxter Lie groupRota-Baxter Lie groupoid

Mathematics Subject Classification ID

Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Integration on manifolds; measures on manifolds (58C35) Groups and algebras in quantum theory and relations with integrable systems (81R12) Lie algebras of Lie groups (22E60) Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items (24)

Cohomology and deformations of weighted Rota–Baxter operators ⋮ Deformations and cohomologies of relative Rota-Baxter operators on Lie algebroids and Koszul-Vinberg structures ⋮ Symmetric skew braces and brace systems ⋮ Twisting theory, relative Rota-Baxter type operators and \(L_\infty\)-algebras on Lie conformal algebras ⋮ Extensions and automorphisms of Rota-Baxter groups ⋮ Skew braces from Rota-Baxter operators: a cohomological characterisation and some examples ⋮ Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects ⋮ Cohomologies of Rota-Baxter Lie triple systems and applications ⋮ Free weighted (modified) differential algebras, free (modified) Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Cohomologies of difference Lie groups and the van Est theorem ⋮ Post-Hopf algebras, relative Rota-Baxter operators and solutions to the Yang-Baxter equation ⋮ Cohomolgies of Rota-Baxter operators on Lie superalgebras and some classifications on Witt superalgebras ⋮ Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases ⋮ Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation ⋮ Rota-Baxter operators on groups ⋮ Lie theory and cohomology of relative Rota–Baxter operators ⋮ Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation ⋮ Rota-Baxter systems and skew trusses ⋮ Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Rota-Baxter groups, skew left braces, and the Yang-Baxter equation ⋮ Deformations, cohomologies and integrations of relative difference Lie algebras

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