University of Illinois Urbana-Champaign

On Hopf Algebra Type and Rational Calculus Decompositions

Bauer, Kristine Baxter

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Description

Title
On Hopf Algebra Type and Rational Calculus Decompositions
Author(s)
Bauer, Kristine Baxter
Issue Date
2001
Doctoral Committee Chair(s)
McCarthy, Randy
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
The second part of my thesis, which is joint work with Randy McCarthy, uses Goodwillie calculus to extend this result to a much larger class of functors. A Hopf algebra A is both an algebra with a multiplication map m:A⊗A→ A and a coalgebra with a comultiplication map D: A→A⊗A which must behave well with respect to each other. Mimicking this definition, we say that an object X of any category which has coproducts, ∨ , is of Hopf algebra type if there is a map 1:X→X∨X which acts like the comultiplication with respect to the fold map, which acts like the multiplication. Randy McCarthy and I have been able to show that rationally, the Goodwillie calculus tower of homotopy functors evaluated on objects of Hopf algebra type split, providing a decomposition. Furthermore, this decomposition generalizes the decomposition of higher Hochschild homology of Part I. Other examples include the cohomology of loop spaces and the Poincare-Birkhoff Witt theorem for Lie algebras over fields of characteristic zero.
Graduation Semester
2001
Type of Resource
text
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http://hdl.handle.net/2142/86772

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