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Differential Algebra Structures on Familes of Trees

Robert L Grossman·Richard G Larson
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Abstract

It is known that the vector space spanned by labeled rooted trees forms a Hopf algebra. Let k be a field and let R be a commutative k-algebra. Let H denote the Hopf algebra of rooted trees labeled using derivations D in Der(R). In this paper, we introduce a construction which gives R a H-module algebra structure and show this induces a differential algebra structure of H acting on R. The work here extends the notion of a R/k-bialgebra introduced by Nichols and Weisfeiler.

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BibTeXRIS

Robert L Grossman, Richard G Larson. 2004-09-01. Differential Algebra Structures on Familes of Trees. https://arxiv.org/abs/math/0409006

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