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SUMMARY:Coordinatization of Countable MV algebras - Philip Scott (Universi
 ty of Ottawa)
DTSTART:20161108T141500Z
DTEND:20161108T151500Z
UID:TALK68629@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:The algebras of many-valued Lukasiewicz logics (MV algebras)\n
 as well as the algebras of quantum measurement (Effect algebras) have\nund
 ergone major development since the 1980s and 1990s.  They have recently\na
 ttracted the attention of categorists.\n\nI will give a brief introduction
  to MV algebras\, as well as the more\ngeneral world of effect algebras. T
 ime permitting\, I hope to illustrate\nthese notions by sketching recent r
 esults (with Mark Lawson\,\nHeriot-Watt) on coordinatization of countable 
 MV-algebras using inverse\nsemigroup theory.  The structures involved\, Bo
 olean inverse monoids\,\nhave recently arisen in areas related to non-comm
 utative Stone duality\,\naperiodic tilings\, etc.  We prove that every cou
 ntable MV algebra is\nisomorphic to the lattice of principal ideals of cer
 tain Boolean inverse\nmonoids.  The specific class involved in the proof\,
  AF inverse monoids\,\ncorresponds to AF C*-algebras and arises from Bratt
 eli diagrams of\ncountable dimension groups.  If there's time\, further ne
 w directions by\nF. Wehrung\, D. Mundici\, et. al. will be discussed.
LOCATION:MR5\, Centre for Mathematical Sciences
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