Results 11 to 20 of about 184 (133)
Rota–Baxter Operators on Dihedral and Alternating Groups [PDF]
Advances in Group Theory and ApplicationsRota–Baxter operators on algebras, which appeared in 1960, have connections with different versions of the Yang–Baxter equation, pre- and postalgebras, double Poisson algebras, etc. In 2020, the notion of Rota–Baxter operator on a group was defined by L.
Alexey Galt, Vsevolod Gubarev
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Lie theory and cohomology of relative Rota–Baxter operators
Journal of the London Mathematical Society, Volume 109, Issue 2, February 2024.Abstract In this paper, we establish a local Lie theory for relative Rota–Baxter operators of weight 1. First we recall the category of relative Rota–Baxter operators of weight 1 on Lie algebras and construct a cohomology theory for them. We use the second cohomology group to study infinitesimal deformations of relative Rota–Baxter operators and ...
Jun Jiang, Yunhe Sheng, Chenchang Zhu
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Rota–Baxter Operators on Cocommutative Weak Hopf Algebras
Mathematics, 2021 In this paper, we first introduce the concept of a Rota–Baxter operator on a cocommutative weak Hopf algebra H and give some examples. We then construct Rota–Baxter operators from the normalized integral, antipode, and target map of H.
Zhongwei Wang +3 more
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Rota–Baxter Operators on Unital Algebras [PDF]
Moscow Mathematical Journal, 2021 We state that all Rota-Baxter operators of nonzero weight on Grassmann algebra over a field of characteristic zero are projections on a subalgebra along another one. We show the one-to-one correspondence between the solutions of associative Yang-Baxter equation and Rota-Baxter operators of weight zero on the matrix algebra $M_n(F)$ (joint with P ...
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Workplace support for newly qualified doctors and secondary school teachers: A comparative analysis
British Educational Research Journal, Volume 49, Issue 5, Page 1005-1043, October 2023., 2023 Abstract Doctors and teachers in their first year of practice face steep learning curves and increased stress, which can induce poor mental health, burnout and attrition. Informal workplace support from colleagues can help smooth transitions and aid professional development.
Helen Foster‐Collins +2 more
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The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators
Journal of Mathematical Physics, 2022 A relative Rota–Baxter algebra is a triple (A, M, T) consisting of an algebra A, an A-bimodule M, and a relative Rota–Baxter operator T. Using Voronov’s derived bracket and a recent work of Lazarev, Sheng, and Tang, we construct an L∞[1]-algebra whose Maurer–Cartan elements are precisely relative Rota–Baxter algebras.
Apurba Das, Satyendra Kumar Mishra
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On rings of differential Rota–Baxter operators [PDF]
International Journal of Algebra and Computation, 2018 Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota–Baxter operator. In applying the general framework to univariate polynomials, one is led to the integro–differential analogs of the classical Weyl algebra.
Xing Gao 0006 +2 more
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A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras
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
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Rota–Baxter Operators on Quadratic Algebras [PDF]
Mediterranean Journal of Mathematics, 2018 We prove that all Rota-Baxter operators on a quadratic division algebra are trivial. For nonzero weight, we state that all Rota-Baxter operators on the simple odd-dimensional Jordan algebra of bilinear form are projections on a subalgebra along another one. For weight zero, we find a connection between the Rota-Baxter operators and the solutions to the
Benito, Pilar +3 more
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Equine Veterinary Education, Volume 34, Issue 7, Page e274-e281, July 2022., 2022 Summary This report describes the successful surgical stabilisation of elbow joint luxation using knotless bone anchors and FiberTape to repair the medial collateral ligament in an 11‐year‐old mare (Case 1) and both medial and lateral collateral ligaments in a 3‐month‐old foal (Case 2).
G. Fridel +4 more
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