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SUMMARY:Roberto Hernández Palomares (Texas A&M University\, USA)
DTSTART:20220627T140000Z
DTEND:20220627T150000Z
DTSTAMP:20260422T180959Z
UID:QGS/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/63/">Q-s
 ystems and higher unitary idempotent completion for C*-algebras</a>\nby Ro
 berto Hernández Palomares (Texas A&M University\, USA) as part of Quantum
  Groups Seminar [QGS]\n\n\nAbstract\nQ-systems were introduced by Longo to
  study finite index inclusions of infinite von Neumann factors. A Q-system
  is a unitary version of a Frobenius algebra object in a tensor category o
 r a C* 2-category. By the work of Müger\, Q-systems give an axiomatizatio
 n of the standard invariant of a finite index subfactor.\n\nFollowing work
  of Douglass-Reutter\, a Q-system is also a unitary version of a higher id
 empotent. In this talk\, we will describe a higher unitary idempotent comp
 letion for C* 2-categories called Q-system completion.\n\nOur main goal is
  to show that C*Alg\, the C* 2-category of right correspondences of unital
  C*-algebras is Q-system complete. To do so\, we will use the graphical ca
 lculus for C* 2-categories\, and adapt a subfactor reconstruction techniqu
 e called realization\, which is inverse to Q-system completion. This resul
 t allows for the straightforward adaptation of subfactor results to C*-alg
 ebras\, characterizing finite index extensions of unital C*-algebras equip
 ped with a faithful conditional expectation in terms of the Q-systems in C
 *Alg. If time allows\, we will discuss an application to induce new symmet
 ries of C*-algebras from old via Q-system completion.\n\nThis is joint wor
 k with Q. Chen\, C. Jones and D. Penneys (arXiv: 2105.12010).\n
LOCATION:https://researchseminars.org/talk/QGS/63/
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