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McCarthy, Randy Bauer, Kristine Baxter 2015-09-28T15:19:26Z 2015-09-28T15:19:26Z 10000-01-01 2001 2001 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&otimes;A→ A and a coalgebra with a comultiplication map D: A→A&otimes;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, &or; , is of Hopf algebra type if there is a map 1:X→X&or;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. Made available in DSpace on 2015-09-28T15:19:26Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3017019.pdf: 3252754 bytes, checksum: eea45836fa41fcfe137a3c1f19704969 (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88053 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 89 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86772 (MiAaPQ)AAI3017019 eng Mathematics On Hopf Algebra Type and Rational Calculus Decompositions text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.