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    ON REPRESENTATION THEORY OF FINITE-DIMENSIONAL HOPF ALGEBRAS

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    Genre
    Thesis/Dissertation
    Date
    2017
    Author
    Jacoby, Adam Michael
    Advisor
    Lorenz, Martin, 1951-
    Committee member
    Lorenz, Martin, 1951-
    Walton, Chelsea
    Dolgushev, Vasily
    Riseborough, Peter
    Department
    Mathematics
    Subject
    Mathematics
    Adjoint Representation
    Frobenius Divisibility
    Hopf Algebra
    Representation Theory
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/1516
    
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    DOI
    http://dx.doi.org/10.34944/dspace/1498
    Abstract
    Representation theory is a field of study within abstract algebra that originated around the turn of the 19th century in the work of Frobenius on representations of finite groups. More recently, Hopf algebras -- a class of algebras that includes group algebras, enveloping algebras of Lie algebras, and many other interesting algebras that are often referred to under the collective name of ``quantum groups'' -- have come to the fore. This dissertation will discuss generalizations of certain results from group representation theory to the setting of Hopf algebras. Specifically, our focus is on the following two areas: Frobenius divisibility and Kaplansky's sixth conjecture, and the adjoint representation and the Chevalley property.
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