### Title page for ETD etd-10312011-200227

Type of Document Dissertation
Author Vega, Maria
URN etd-10312011-200227
Title Twisted Frobenius-Schur Indicators for Hopf Algebras
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Sage, Daniel Committee Chair
Achar, Pramod Committee Member
Cohen, Daniel Committee Member
Shipman, Stephen Committee Member
Kirshner, David Dean's Representative
Keywords
• Frobenius-Schur indicator
• automorphism
• semisimple Hopf algebra
• character
Date of Defense 2011-05-16
Availability unrestricted
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.

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