Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras

Yi Zhang, Xiaosong Peng and Yuanyuan Zhang
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Yi Zhang: School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China
Xiaosong Peng: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Yuanyuan Zhang: School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

Mathematics, 2022, vol. 10, issue 2, 1-15

Abstract: As a generalization of Rota–Baxter algebras, the concept of an Ω -Rota–Baxter could also be regarded as an algebraic abstraction of the integral analysis. In this paper, we introduce the concept of an Ω -dendriform algebra and show the relationship between Ω -Rota–Baxter algebras and Ω -dendriform algebras. Then, we provide a multiplication recursion definition of typed, angularly decorated rooted trees. Finally, we construct the free Ω -Rota–Baxter algebra by typed, angularly decorated rooted trees.

Keywords: Rota–Baxter algebra; rooted tree; operated algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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