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Hsiang-Ping Huang

2009-06-23
14:00:00 - 15:30:00

From group to subfactor

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, I will start from the regular representation of G= {\mathbb Z}, and develop two non-isomorphic crossed products (with or without cocycles): G by another copy of G. It is equivalent to the ergodic theory of measures. Or you may imagine it as the discrete case of momentum operator, and position operator. The noncommutative view leads us to the unital *-algebra with a trace, M. A factor M is nothing but the center of M is trivial, i.e., {\mathbb C}. Subfactor theory is a generalization of Galois theory for group. The central question is "to be or not to be a group". Easily you would guess the answer is definitely not. I will provide an example in the graphic way called planar algebra. How to generate an "exotic" subfactor is a very interesting and intriguing question. In a different dictionary, you may call it topological quantum field theory (TQFT).