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Jose Cervantes Thesis.pdf (475.9 KB)
ETD Abstract Container
Abstract Header
Hopf algebras associated to transitive pseudogroups in codimension 2
Author Info
Cervantes, José Rodrigo
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1452041006
Abstract Details
Year and Degree
2016, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
We associate two different Hopf algebras to the same transitive but not primitive pseudogrup of local diffeomorphisms on R
2
leaving invariant the trivial foliation where we identify R
2
as a product of lines R
1
x R
1
. 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.
Committee
Henri Moscovici (Advisor)
James Cogdell (Committee Member)
Thomas Kerler (Committee Member)
Ruth Lowery (Other)
Pages
89 p.
Subject Headings
Mathematics
Keywords
Hopf algebras
;
Hopf cyclic cohomology
;
Bicrossed Product
;
Lie algebra cohomology
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Citations
Cervantes, J. R. (2016).
Hopf algebras associated to transitive pseudogroups in codimension 2
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1452041006
APA Style (7th edition)
Cervantes, José.
Hopf algebras associated to transitive pseudogroups in codimension 2.
2016. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1452041006.
MLA Style (8th edition)
Cervantes, José. "Hopf algebras associated to transitive pseudogroups in codimension 2." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1452041006
Chicago Manual of Style (17th edition)
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Document number:
osu1452041006
Download Count:
412
Copyright Info
© 2016, some rights reserved.
Hopf algebras associated to transitive pseudogroups in codimension 2 by José Rodrigo Cervantes is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.