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REPRESENTATIONS OF FINITE DIMENSIONAL HOPF ALGEBRAS
by
Andrea Jedwab
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2008
Copyright 2008 Andrea Jedwab
Object Description
| Title | Representations of finite dimensional Hopf algebras |
| Author | Jedwab, Andrea |
| Author email | jedwab@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-05-05 |
| Date submitted | 2008 |
| Restricted until | Restricted until 18 July 2008. |
| Date published | 2008-07-18 |
| Advisor (committee chair) | Montgomery, Susan |
| Advisor (committee member) |
Guralnick, Robert Pilch, Krzysztof |
| Abstract | Frobenius-Schur indicators are one of few invariants in the study of Hopf algebras. In the first part of this work we study two dual families of Hopf algebras Hn = k^{C_n}#k_S_{n-1} and Jn = k^S_{n-1}#k_{C_n}, constructed from factorizations of the symmetric group. We determine the Frobenius-Schur indicators of the representations of those bismash products, in an attempt to determine whether, as is the case for the symmetric group, these Hopf algebras are totally orthogonal. While we conclude that the first family is totally orthogonal, we prove that the other one is not.; In the second part of this work we introduce a concept of indicator for the irreducible representations of Hopf algebras that are not necessarily semisimple. This definition generalizes the one for semisimple Hopf algebras and maintains some of its properties. We then study the irreducible representations of the Drinfeld doubles of the Taft algebras and compute the values of their indicators, by considering the projection of the double onto u_q(sl_2). |
| Keyword | Hopf algebras; Schur indicator |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m1357 |
| Rights | Jedwab, Andrea |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Jedwab-20080718 |
| Archival file | uscthesesreloadpub_Volume14/etd-Jedwab-20080718.pdf |
Description
| Title | Page 1 |
| Full text | REPRESENTATIONS OF FINITE DIMENSIONAL HOPF ALGEBRAS by Andrea Jedwab A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2008 Copyright 2008 Andrea Jedwab |
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