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CATEGORIES:Category Theory Seminar
SUMMARY:Coordinatization of Countable MV algebras - Philip
Scott (University of Ottawa)
DTSTART;TZID=Europe/London:20161108T141500
DTEND;TZID=Europe/London:20161108T151500
UID:TALK68629AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68629
DESCRIPTION:The algebras of many-valued Lukasiewicz logics (MV
algebras)\nas well as the algebras of quantum mea
surement (Effect algebras) have\nundergone major d
evelopment since the 1980s and 1990s. They have r
ecently\nattracted the attention of categorists.\n
\nI will give a brief introduction to MV algebras\
, as well as the more\ngeneral world of effect alg
ebras. Time permitting\, I hope to illustrate\nthe
se notions by sketching recent results (with Mark
Lawson\,\nHeriot-Watt) on coordinatization of coun
table MV-algebras using inverse\nsemigroup theory.
The structures involved\, Boolean inverse monoid
s\,\nhave recently arisen in areas related to non-
commutative Stone duality\,\naperiodic tilings\, e
tc. We prove that every countable MV algebra is\n
isomorphic to the lattice of principal ideals of c
ertain Boolean inverse\nmonoids. The specific cla
ss involved in the proof\, AF inverse monoids\,\nc
orresponds to AF C*-algebras and arises from Bratt
eli diagrams of\ncountable dimension groups. If t
here's time\, further new directions by\nF. Wehrun
g\, D. Mundici\, et. al. will be discussed.
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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