An Algebraic Study of Multivariable Integration and Linear Substitution
Rings and Algebras
2020-07-27 v1
Abstract
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 Groebner basis for the ideal they generate.
Cite
@article{arxiv.1503.01694,
title = {An Algebraic Study of Multivariable Integration and Linear Substitution},
author = {Markus Rosenkranz and Xing Gao and Li Guo},
journal= {arXiv preprint arXiv:1503.01694},
year = {2020}
}
Comments
44 pages, 1 table