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On Integro-Differential Algebras
Published 3 Dec 2012 in math.RA, math.AC, and math.CA | (1212.0266v1)
Abstract: 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.
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