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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Kenichi Shimizu\, Shibaura Institute of Technology\n\nAbstract:
\nA modular tensor category is an interesting class of tensor categories st
udied from the viewpoint of\, e\,g.\, representation theory\, low-dimension
al topology\, quantum physics and quantum computing. Although a modular ten
sor category is defined to be a semisimple\ntensor category with some extra
structures\, we are interested in a "non-semisimple" generalization of a m
odular tensor category. We expect such a "non-semisimple" modular tensor ca
tegory gives a new perspective for the above-mentioned areas of mathematics
and mathematical physics.\n\nIn this talk\, I will review recent developme
nts on the study of "non-semisimple" modular tensor categories and their ap
plications. We shall remark that a non-semisimple analogue of a modular ten
sor category has been introduced by Lyubashenko in mid 90's. I will\,\nespe
cially\, talk about the fact that a ribbon finite tensor category C is modu
lar (in the sense of Lyubashenko) if and only if the Mueger center of C is
trivial. This fact allows us to give new examples of non-semisimple modular
tensor categories. For the proof of this fact\, we need some categorical t
echniques originating from the theory of Hopf algebras: the character theor
y and the integral theory.
DTEND:20200113T230000Z
DTSTAMP:20201030T113330Z
DTSTART:20200113T220000Z
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 245
SEQUENCE:0
SUMMARY:Geometry/Topology/Categorification Seminar: Recent developments of
non-semisimple modular tensor categories
UID:tag:localist.com\,2008:EventInstance_32371812776042
URL:https://calendar.usc.edu/event/geometrytopologycategorification_seminar
_recent_developments_of_non-semisimple_modular_tensor_categories
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