Cauchy's theorem for Hopf algebras
Abstract
Cauchy's
theorem states that a finite group contains an element of prime order for every
prime that divides the order of the group. Since the exponent of a group is the
least common multiple of the orders of all its elements, this can be
reformulated by saying that a prime that divides the order of a group also
divides its exponent. It was an open conjecture by P. Etingof
and S. Gelaki that this result, in this formulation,
holds also for semisimple Hopf
algebras. In this talk, we present a proof of this conjecture, which is joint
work with Y. Kashina and Y. Zhu.
The
talk is intended for a general audience; in particular, no knowledge of Hopf algebras will be assumed. We will therefore begin by
explaining what a Hopf
algebra is and how the exponent of a Hopf algebra can
be defined. We will then explain how the analogue of Cauchy's theorem can be deduced
from the theory of higher Frobenius-Schur indicators.
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Room 517, Meng Wah Complex, HKU |
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All are welcome |
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