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Title:  On Hopf Algebra Type and Rational Calculus Decompositions 
Author(s):  Bauer, Kristine Baxter 
Doctoral Committee Chair(s):  McCarthy, Randy 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
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 PoincareBirkhoff Witt theorem for Lie algebras over fields of characteristic zero. 
Issue Date:  2001 
Type:  Text 
Language:  English 
Description:  89 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2001. 
URI:  http://hdl.handle.net/2142/86772 
Other Identifier(s):  (MiAaPQ)AAI3017019 
Date Available in IDEALS:  20150928 
Date Deposited:  2001 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois