Identifier
etd-10312011-200227
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
The classical Frobenius--Schur indicators for finite groups are character sums defined for any representation and any integer $m\ge 2$. In the familiar case $m=2$, the Frobenius--Schur indicator partitions the irreducible representations over the complex numbers into real, complex, and quaternionic representations. In recent years, several generalizations of these invariants have been introduced. Bump and Ginzburg in 2004, building on earlier work of Mackey from 1958, have defined versions of these indicators which are twisted by an automorphism of the group. In another direction, Linchenko and Montgomery in 2000 defined Frobenius--Schur indicators for finite dimensional semisimple Hopf algebras. In this dissertation, we construct twisted Frobenius--Schur indicators for semisimple Hopf algebras; these include all of the above indicators as special cases and have similar properties.
Date
2011
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Vega, Maria, "Twisted Frobenius-Schur indicators for Hopf algebras" (2011). LSU Doctoral Dissertations. 1590.
https://repository.lsu.edu/gradschool_dissertations/1590
Committee Chair
Sage, Daniel
DOI
10.31390/gradschool_dissertations.1590