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- W4385963400 abstract "Differential operators and integral operators are linked together by the first fundamental theorem of calculus. Based on this principle, the notion of a differential Rota-Baxter algebra was proposed by Guo and Keigher from an algebraic abstraction point of view. Recently, the subject has attracted more attention since it is associated with many areas in mathematics, such as integro-differential algebras. This paper considers differential algebras, Rota-Baxter algebras and differential Rota-Baxter algebras in the quasi-idempotent operator context. We establish a Grobner-Shirshov basis for free commutative quasi-idempotent differential algebras (resp. Rota-Baxter algebras, resp. differential Rota-Baxter algebras). This provides a linear basis of free object in each of the three corresponding categories by Composition-Diamond lemma." @default.
- W4385963400 created "2023-08-18" @default.
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- W4385963400 date "2023-07-08" @default.
- W4385963400 modified "2023-09-23" @default.
- W4385963400 title "Construction of free quasi-idempotent differential Rota-Baxter algebras by Grobner-Shirshov bases" @default.
- W4385963400 doi "https://doi.org/10.48550/arxiv.2308.00602" @default.
- W4385963400 hasPublicationYear "2023" @default.
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