Classification of monomial Rota–Baxter operators on k[x]

DOI10.1142/S0219498816500870zbMath1346.16043arXiv1503.02606OpenAlexW2963304292MaRDI QIDQ2801832

Houyi Yu

Publication date: 22 April 2016

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.02606

zbMATH Keywords

polynomial algebrasRota-Baxter operatorsmonomial linear operators

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Generalizations of commutativity (associative rings and algebras) (16U80) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Integral operators (47G10) Abstract integral equations, integral equations in abstract spaces (45N05) Associative rings and algebras with additional structure (16W99)

Related Items (7)

Modules of non-unital polynomial Rota-Baxter algebras ⋮ Monomial Rota-Baxter operators of nonzero weight on \(F[x, y\) coming from averaging operators] ⋮ Monomial Rota-Baxter operators on free commutative non-unital algebra ⋮ Injective Rota-Baxter operators of weight zero on \(F[x\)] ⋮ Rota-type operators on 3-dimensional nilpotent associative algebras ⋮ Rota-type operators on null-filiform associative algebras ⋮ Rota-Baxter operators on unital algebras

Cites Work

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• Rota-Baxter operators on Witt and Virasoro algebras
• An analytic problem whose solution follows from a simple algebraic identity
• Spitzer's identity and the algebraic Birkhoff decomposition in pQFT
• Rota-Baxter operators on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) and solutions of the classical Yang-Baxter equation

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