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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 Urbana-Champaign
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 Poincare-Birkhoff 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 Urbana-Champaign, 2001.
URI:http://hdl.handle.net/2142/86772
Other Identifier(s):(MiAaPQ)AAI3017019
Date Available in IDEALS:2015-09-28
Date Deposited:2001


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