2021
DOI: 10.17323/1609-4514-2021-21-2-325-364
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Rota–Baxter Operators on Unital Algebras

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Cited by 13 publications
(35 citation statements)
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“…We continue investigations fulfilled by S. de Bragança in 1975 [6] and by H. An and C. Bai in 2008 [1]. Since all RB-operators on A of weight zero are trivial [12], i.e., equal to 0, we study only RB-operators on A of nonzero weight λ.…”
Section: Introductionmentioning
confidence: 82%
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“…We continue investigations fulfilled by S. de Bragança in 1975 [6] and by H. An and C. Bai in 2008 [1]. Since all RB-operators on A of weight zero are trivial [12], i.e., equal to 0, we study only RB-operators on A of nonzero weight λ.…”
Section: Introductionmentioning
confidence: 82%
“…Proof. If λ = 0, then R = 0 [12] and x • R y = 0. For λ = 0, we may assume that λ = 1, since rescalling of the product does not exchange the algebraic structure.…”
Section: Rb-induced Algebra Structures On a Sum Of Fieldsmentioning
confidence: 99%
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“…This notion firstly appeared in the article [21] of F. Tricomi in 1951 and further was several times rediscovered [5,6], see the monograph [10]. Let us mention the bijection [1,9,18] between RB-operators of weight 0 on the matrix algebra and its solutions of the associative Yang Baxter equation (AYBE) [3,17,24]. We state the correspondence between countable-dimensional double Lie algebras V and Rota Baxter operators acting from the space of finitary matrices [4] to End(V ) and satisfying some additional finiteness conditions.…”
Section: Introductionmentioning
confidence: 99%