Results 11 to 20 of about 455,961 (135)
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 Leibniz Algebras and Their Constructions
Advances in Mathematical Physics, Volume 2018, Issue 1, 2018., 2018 In this paper, we introduce the concept of Rota‐Baxter Leibniz algebras and explore two characterizations of Rota‐Baxter Leibniz algebras. And we construct a number of Rota‐Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota‐Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra.
Liangyun Zhang +3 more
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Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras
MathematicsIn this paper, we establish the cohomology of relative Rota–Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then, we use this type of cohomology to characterize deformations of relative Rota–Baxter operators on Lie-Yamaguti ...
Jia Zhao, Yu Qiao
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Rota–Baxter Operators on Skew Braces
MathematicsIn this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as (Z,+,∘) and (Z/(4),+,∘).
Ximu Wang +2 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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Rota-Baxter operators and Bernoulli polynomials [PDF]
, 2021 summary:We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and ...
Gubarev, Vsevolod
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Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras [PDF]
, 2023 A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$.
Saha, Ripan +3 more
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Deformations and Homotopy Theory of Relative Rota-Baxter Lie Algebras [PDF]
, 2021 We determine the L∞-algebra that controls deformations of a relative Rota–Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying LieRep pair by the dg Lie algebra controlling deformations of ...
Lazarev, Andrey +2 more
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Rota-Baxter operators on the polynomial algebras, integration and averaging operators [PDF]
, 2014 The concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x] k[x] .
Guo, Li +5 more
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