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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Algebra and Number Theory
- Rota-Baxter algebra
- noncommutative Gröbner-Shirshov basis