Constructions of free commutative integro-differential algebras
Xing Gao, Li Guo
TL;DR
This paper surveys two recent methods for constructing free commutative integro-differential algebras, utilizing Rota-Baxter algebra techniques and algebraic bases, advancing the algebraic understanding of these structures.
Contribution
It introduces two novel constructions of free commutative integro-differential algebras using evaluations and Gr"obner-Shirshov bases methods.
Findings
Two constructions of free commutative integro-differential algebras are outlined.
The methods are based on mixable shuffles and algebraic bases.
The survey clarifies the algebraic structures and techniques involved.
Abstract
In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras by mixable shuffles. The first is by evaluations. The second is by the method of Gr\"obner-Shirshov bases.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons