An algebraic study of multivariable integration and linear substitution

Markus Rosenkranz, Xing Gao, Li Guo

Research output: Contribution to journalArticlepeer-review


We set up an algebraic theory of multivariable integration, based on a hierarchy of Rota-Baxter operators and an action of the matrix monoid as linear substitutions. Given a suitable coefficient domain with a bialgebra structure, this allows us to build an operator ring that acts naturally on the given Rota-Baxter hierarchy. We conjecture that the operator relations are a noncommutative Gröbner-Shirshov basis for the ideal they generate.

Original languageEnglish (US)
Article number1950207
JournalJournal of Algebra and its Applications
Issue number11
StatePublished - Nov 1 2019

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


  • Rota-Baxter algebra
  • bialgebra
  • coalgebra
  • noncommutative Gröbner-Shirshov basis


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