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SUMMARY:Induced C*-hulls for *-algebras - Ralf Meyer (Georg-August-Univers
 ität Göttingen)
DTSTART:20170615T103000Z
DTEND:20170615T113000Z
UID:TALK72929@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Let A be a *-algebra that is graded by a group G with fibres A
 _g for g in G.&nbsp\; Assume that we have found a C*-algebra B_e whose &ld
 quo\;representations&rdquo\; are &ldquo\;equivalent&rdquo\; to the &ldquo\
 ;integrable&rdquo\; &ldquo\;representations&rdquo\; of the unit fibre A_e.
 &nbsp\; Call a &ldquo\;representation&rdquo\; of A  &ldquo\;integrable&rdq
 uo\;\, if its restriction to A_e is &ldquo\;integrable&rdquo\;.&nbsp\; Und
 er some assumptions\, the &ldquo\;integrable&rdquo\; &ldquo\;representatio
 ns&rdquo\; of A are &ldquo\;equivalent &rdquo\; to the &ldquo\;representat
 ions&rdquo\; of a certain C*-algebra B constructed from B_e and the graded
  *-algebra A.&nbsp\; The C*-algebra B is the section C*-algebra of a Fell 
 bundle over G.&nbsp\; The words in quotation marks have to be interpreted 
 carefully to make this true.&nbsp\; In particular\, representations must b
 e understood to take place on Hilbert modules\, not just Hilbert spaces\, 
 and the equivalence is required natural with respect to induction of repre
 sentations and isometric intertwiners.&nbsp\; Under some commutativity ass
 umptions\, the main result of my lecture has been proved by Savchuk and Sc
 hm&uuml\;dgen\, who also give several examples.&nbsp\; A sample of the res
 ult concerns Weyl algebras and twisted Weyl algebras in countably many gen
 erators.&nbsp\; These come with a canonical grading by the free Abelian gr
 oup on countably many generators.<br>
LOCATION:Seminar Room 1\, Newton Institute
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