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CATEGORIES:Lecture, Colloquia, Seminar
DESCRIPTION:Speaker: Konrad Aguilar (Arizona State University)\n\nTitle: Qu
antum metrics on the tensor product of a commutative C*-algebra and an AF
C*-algebra\n\nAbstarct: Quantum metric spaces were introduced in 1998 by M.
A. Rieffel as noncommutative analogues to metric spaces to study the metri
c aspects of Noncommutative Geometry of A. Connes. In this talk\, given a c
ompact metric space X and a unital AF (approximately finite-dimensional) C*
-algebra A equipped with a faithful tracial state\, we place quantum metric
s on the tensor product of C(X) and A given established quantum metrics o
n C(X) and A from work with Bice and Latremoliere. We prove the inductive
limit of C(X) tensor A given by A is a metric limit in the Gromov-Hausdorff
propinquity\, which is a noncommutative analogue to the Gromov-Hausdorff d
istance on the class of compact metric spaces. We show that our quantum met
ric is compatible with the tensor product by producing a Leibniz rule on el
ementary tensors and showing the diameter of our quantum metric on the tens
or product is bounded above the diameter of the Cartesian product of the q
uantum metric spaces. Finally\, we provide continuous families in the Grom
ov-Hausdorff propinquity of C(X) tensor A\, which extends our previous resu
lts with Latremoliere on UHF algebras. We will define many of the terms use
d in this talk including quantum metric spaces and C*-algebras.
DTEND:20191022T212000Z
DTSTAMP:20191210T222303Z
DTSTART:20191022T203000Z
LOCATION:CW 120
SEQUENCE:0
SUMMARY:Analysis Seminar. Konrad Aguilar. Quantum metrics on the tensor pr
oduct of a commutative C*-algebra and an AF C*-algebra
UID:tag:localist.com\,2008:EventInstance_31635043277732
URL:https://events.k-state.edu/event/analysis_seminar_konrad_aguilar_quantu
m_metrics_on_the_tensor_product_of_a_commutative_c-algebra_and_an_af_c-alge
bra
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