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Rota–Baxter operators on groups
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2023 Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of Rota-Baxter operators on a group. Given a map on a group, we study its extensions to a Rota-Baxter operator.
Vsevolod Gubarev +2 more
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RELATIVE ROTA–BAXTER OPERATORS AND TRIDENDRIFORM ALGEBRAS
Journal of Algebra and Its Applications, 2013A relative Rota–Baxter operator is a relative generalization of a Rota–Baxter operator on an associative algebra. In the Lie algebra context, it is called an [Formula: see text]-operator, originated from the operator form of the classical Yang–Baxter equation. We generalize the well-known construction of dendriform and tridendriform algebras from Rota–
Bai, Chengming, Guo, Li, Ni, Xiang
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Relative Rota–Baxter Operators on Groups and Hopf Algebras
Bulletin of the Iranian Mathematical SocietyM. Goncharov introduced and studied a Rota--Baxter operator on a cocommutative Hopf algebra. In the present paper we define relative Rota--Baxter operators on an arbitrary Hopf algebra. A particular case of this definition is Goncharov's operator. On a Hopf algebra with a relative Rota--Baxter operator we define new associative operation and construct ...
Valeriy G Bardakov, Bardakov Valeriy G
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Rota–Baxter Operators on the Simple Jordan Superalgebra $ D_{t} $
Siberian Mathematical Journal, 2022In Kac's classification of the finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic \(0\), besides the natural infinite families associated to quadratic superforms and associative superalgebras with a superinvolution, there appear three exceptions: the tiny Kaplansky superalgebra \(K_3\) of dimension \(3\), which
T. A. Bolotina, V. Yu. Gubarev
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Extended Rota-Baxter Operators on Leibniz Algebras
Frontiers of MathematicsDingguo Wang, Wang Dingguo
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Homogeneous Rota-Baxter operators on $A_ω$ (II)
201617 ...
Bai, Ruipu, Zhang, Yinghua
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Rota–Baxter operators on the semi-quaternion algebra
Journal of Algebra and Its ApplicationsIn this paper, we shall discuss Rota–Baxter operators on the semi-quaternion algebra, and give all Rota–Baxter operators of any weight.
Quanguo Chen, Yong Deng
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Rota-Baxter Operators of Nonzero Weight on the Split Octonions
Advances in Applied Clifford AlgebraszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rota—Baxter groups, skew left braces, and the Yang—Baxter equation
Journal of Algebra, 2022Vsevolod Gubarev, Valeriy G Bardakov
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Rota–Baxter operators of nonzero weight on the matrix algebra of order three
Linear and Multilinear Algebra, 2022Maxim Goncharov, Vsevolod Gubarev
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