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DESCRIPTION:How amenable are amenable operator algebras?\n\nAmenability is 
 a property both of von Neumann algebras and of C*-algebras\, with an appro
 priate definition in each case. A discrete group is amenable in the classi
 cal sense if\, and only if\, all the C*-algebras and von Neumann algebras 
 generated by it are amenable. (For a more general locally compact group th
 e situation is a bit more subtle.) There are many equivalent definitions o
 f amenability for both C*-algebras and von Neumann algebras. In addition\,
  a C*-algebra is amenable if\, and only if\, all the von Neumann algebras 
 generated by it (in representations) are amenable. Every amenable von Neum
 ann algebra is generated by some amenable C*-algebra. Amazingly\, even tho
 ugh the classification of either amenable von Neumann algebras or amenable
  C*-algebras might\, on the face of it\, even with appropriate countabilit
 y assumptions\, threaten to be just as complicated as that of amenable gro
 ups---which is surely hopeless---even in the abelian case!---\, in fact\, 
 amenable von Neumann algebras are completely classified by a simple invari
 ant\, and recently (but with a long history) there is an analogous result 
 for amenable C*-algebras---with a certain additional well-behavedness prop
 erty that is quite simple to state. Most (or at least many!) naturally occ
 urring C*-algebras or von Neumann algebras are amenable\, just as is true 
 for groups. There are also many\, many examples of amenable C*-algebras wh
 ich are well enough behaved to fit into the recent classification. Indeed\
 , the class in question is just just those simple (separable\, amenable) C
 *-algebras that absorb tensorially a certain one of them\, which in a stro
 ng sense is just a souped-up version of the complex numbers. (There is an 
 additional technical assumption\, which however may hold automatically.) S
 ince this funny algebra of complex numbers absorbs itself\, the tensor pro
 duct of an arbitrary simple separable amenable C*-algebra with it also abs
 orbs it---and is therefore in the classifiable class.\n
DTSTART:20181108T193000Z
DTEND:20181108T203000Z
LOCATION:Room VCH-2810\, CA\, Université Laval
SUMMARY:George A. Elliott\, University of Toronto
URL:https://www.mcgill.ca/mathstat/channels/event/george-elliott-university
 -toronto-291306
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