Results 11 to 20 of about 2,636,434 (156)

Leibniz bialgebras, relative Rota–Baxter operators, and the classical Leibniz Yang–Baxter equation [PDF]

Journal of Noncommutative Geometry, 2022
In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras, and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative) Rota–Baxter operator on a Leibniz algebra and construct the graded Lie algebra that characterizes
Rong Tang, Yunhe Sheng
openaire   +5 more sources

A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras [PDF]

Bulletin of the London Mathematical Society, Volume 54, Issue 6, Page 2045-2065, December 2022., 2022
Abstract In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter (RB$\mathsf {RB}$) Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an L∞$L_\infty$‐algebra whose Maurer–Cartan elements are relative RB$\mathsf {RB}$ Lie algebras.
Yunhe Sheng
wiley   +2 more sources

Relative Rota-Baxter operators, modules and projections

Czechoslovak Mathematical Journal
arXiv admin note: text overlap with arXiv:2404 ...
Fernández Vilaboa, José Manuel, González Rodríguez, Ramón, Ramos Pérez, Brais   +2 more
openaire   +4 more sources

From relative Rota-Baxter operators and relative averaging operators on Lie algebras to relative Rota-Baxter operators on Leibniz algebras: a uniform approach [PDF]

Mathematical Research Letters, 2023
28 pages, to appear in Math.
Sheng, Yunhe, Tang, Rong, Wagemann, Friedrich   +2 more
openaire   +3 more sources

Deformations of relative Rota-Baxter operators on Leibniz Triple Systems [PDF]

, 2022
24pages.
Wu, Xueru, Ma, Yao, Chen, Liangyun
openaire   +3 more sources

Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures

Symmetry, Integrability and Geometry: Methods and Applications, 2022
Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extendability of order n deformations to order n+1 deformations of relative Rota ...
Liu, Meijun, Liu, Jiefeng, Sheng, Yunhe
openaire   +4 more sources

3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras [PDF]

Journal of Algebra, 2023
In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras and $3$-post-Lie algebras. A 3-post-Lie algebra consists of a 3-Lie algebra structure and a ternary operation such that some compatibility conditions are satisfied.
Shuai Hou, Yunhe Sheng, Yanqiu Zhou
openaire   +4 more sources

Relative Rota-Baxter operators of nonzero weights on Lie Triple Systems [PDF]

, 2022
14pages.
Wu, Xueru, Ma, Yao, Chen, Liangyun
openaire   +3 more sources

Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators [PDF]

Forum Mathematicum
Abstract We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang–Baxter equation (CLYBE) whose skew-symmetric parts are invariant. In addition to triangular Leibniz bialgebras, quasi-triangular Leibniz bialgebras contain factorizable Leibniz bialgebras as ...
Chengming Bai, Guilai Liu, Yunhe Sheng, Rong Tang   +3 more
openaire   +3 more sources

Post Lie-Yamaguti algebras, relative Rota-Baxter operators of nonzero weights, and their deformations [PDF]

, 2023
arXiv admin note: substantial text overlap with arXiv:2303 ...
Qiao, Yu, Xu, Senrong, Zhao, Jia
openaire   +3 more sources