Algebraic Combinatorics Seminar
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UNIVERSITY OF KENTUCKY **

ALGEBRAIC COMBINATORICS SEMINAR

845 PATTERSON OFFICE TOWER

SPRING 2004

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Positive Hopf Algebras
and the Set Theoretical Yang-Baxter Equation

Professor Min Yan

The Hong Kong University of Science and Technology

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Friday, January 16, 2004

11:00 am, 845 Patterson Office Tower

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Abstract:

A Hopf algebra is positive if it has a basis with respect to which the
structure constants are non-negative. We give a complete
classification of such Hopf algebras and discuss the positive
quasi-triangular structures on such Hopf algebras. The study of the
positivity condition in Hopf algebras was motivated by the problem of
set-theoretical solutions of the Yang-Baxter equation. We will see how
our results can be used to solve the problem.