2012/12/03 by Li Guo, Georg Regensburger, Markus Rosenkranz · 56 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic differential equation #Algebraic structures and combinatorial models #Computer science #Construct (python library) #Differential (mechanical device) #Differential algebra #Differential algebraic equation #Differential equation #Generator (circuit theory) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Ordinary differential equation #Pure mathematics #math.AC #math.CA #math.RA #msc:12H05 #msc:12H20 #msc:16W99 #msc:34M15 #msc:47G20 #msc:68W30
paper · pdf · doi:10.1016/j.jpaa.2013.06.015
published in Journal of Pure and Applied Algebra 218(3), 456-473 (Elsevier BV) · 26 pages
arxiv created 2012/12/03 · openalex publication_date 2013/07/29 · arxiv updated 2014/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the differential Rota-Baxter algebra. We construct free commutative integro-differential algebras with weight generated by a base differential algebra. This in particular gives an explicit construction of the integro-differential algebra on one generator. Properties of these free objects are studied.