Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras

Xing Gao, Li Guo, Yi Zhang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The Rota-Baxter algebra and the shuffle product are both algebraic structures arising from integral operators and integral equations. Free commutative Rota-Baxter algebras provide an algebraic framework for integral equations with the simple Riemann integral operator. The Zinbiel algebras form a category in which the shuffle product algebra is the free object. Motivated by algebraic structures underlying integral equations involving multiple integral operators and kernels, we study commutative matching Rota-Baxter algebras and construct the free objects making use of the shuffle product with multiple decorations. We also construct free commutative matching Rota-Baxter algebras in a relative context, to emulate the action of the integral operators on the coefficient functions in an integral equation. We finally show that free commutative matching Rota-Baxter algebras give the free matching Zinbiel algebra, generalizing the characterization of the shuffle product algebra as the free Zinbiel algebra obtained by Loday.

Original languageEnglish (US)
Pages (from-to)402-432
Number of pages31
JournalJournal of Algebra
Volume586
DOIs
StatePublished - Nov 15 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Matching Rota-Baxter algebra
  • Matching Zinbiel algebra
  • Matching dendriform algebra
  • Shuffle product with decoration

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