Constructions of free commutative integro-differential algebras

A. Connes; A.I. Shirshov; A.I. Zhukov; C. Bai; E.R. Kolchin; F. Baader; G. Baxter; G.-C. Rota; G.M. Bergman; H. Albrecher; H. Albrecher; H. Hironaka; K. Ebrahimi-Fard; K. Ebrahimi-Fard; L. Guo; L. Guo; L. Guo; L. Guo; L. Guo; L. Guo; L. Guo; L.A. Bokut; L.A. Bokut; L.A. Bokut; L.A. Bokut; M. Hoffman; M. Rosenkranz; M. Rosenkranz; M. Rosenkranz; M.A. Semenov-Tian-Shansky; P. Cartier; P.M. Cohn; W.-T. Wu

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Constructions of free commutative integro-differential algebras

Authors: A. Connes
A.I. Shirshov
A.I. Zhukov
C. Bai
E.R. Kolchin
F. Baader
G. Baxter
G.-C. Rota
G.M. Bergman
H. Albrecher
H. Albrecher
H. Hironaka
K. Ebrahimi-Fard
K. Ebrahimi-Fard
L. Guo
L. Guo
L. Guo
L. Guo
L. Guo
L. Guo
L. Guo
L.A. Bokut
L.A. Bokut
L.A. Bokut
L.A. Bokut
M. Hoffman
M. Rosenkranz
M. Rosenkranz
M. Rosenkranz
M.A. Semenov-Tian-Shansky
P. Cartier
P.M. Cohn
W.-T. Wu
Publication date: 1 January 2014
Publisher
Doi

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.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004

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