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Hopf algebras associated to transitive pseudogroups in codimension 2
Cervantes, José Rodrigo

2016, Doctor of Philosophy, Ohio State University, Mathematics.
We associate two different Hopf algebras to the same transitive but not primitive pseudogrup of local diffeomorphisms on R2 leaving invariant the trivial foliation where we identify R2 as a product of lines R1 x R1.

Their construction is based on ideas used to build the Hopf algebras associated to primitive Lie pseudogroups by Connes-Moscovici and Moscovici-Rangipour. Each of the two Hopf algebras is first defined via its action on the respective crossed product algebra associated to the pseudogroup, and then it is realized as a bicrossed product of a universal enveloping algebra of a Lie algebra and a Hopf algebra of regular functions on a formal group. Using the bicrossed product structure we prove that, although the two Hopf algebras are not isomorphic, they have the same periodic Hopf cyclic cohomology. More precisely, for each of them the periodic Hopf cyclic cohomology is canonically isomorphic to the Gelfand-Fuks cohomology of the infinite dimensional Lie algebra related with the pseudogroup.
Henri Moscovici (Advisor)
James Cogdell (Committee Member)
Thomas Kerler (Committee Member)
Ruth Lowery (Other)
89 p.

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Cervantes, J. (2016). Hopf algebras associated to transitive pseudogroups in codimension 2. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Cervantes, José. "Hopf algebras associated to transitive pseudogroups in codimension 2." Electronic Thesis or Dissertation. Ohio State University, 2016. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Cervantes, José "Hopf algebras associated to transitive pseudogroups in codimension 2." Electronic Thesis or Dissertation. Ohio State University, 2016. https://etd.ohiolink.edu/

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