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SUMMARY:A classification of some 3-Calabi-Yau algebras - Paul Smith (Unive
 rsity of Washington)
DTSTART:20170329T090000Z
DTEND:20170329T100000Z
UID:TALK71691@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:This is a report on joint work with Izuru Mori and work of Mor
 i and Ueyama.<br>A&nbsp\;graded algebra A is Calabi-Yau of dimension n if 
 the homological shift A[n] is a dualizing object in the appropriate derive
 d category. For example\, polynomial rings are Calabi-Yau algebras. Althou
 gh many examples are known\, there are few if any&nbsp\;classification res
 ults. Bocklandt proved that connected graded Calabi-Yau algebras are of th
 e form&nbsp\;TV/(dw) where TV denotes the tensor algebra on a vector space
  V and (dw) is the ideal generated by the cyclic partial derivatives of an
  element w in TV. However\, it is not known exactly which w give rise to a
  Calabi-Yau algebra. We present a classification of those w for which&nbsp
 \;TV/(dw) is Calabi-Yau in two cases:&nbsp\;when dim(V)=3 and w is in V^{\
 \otimes 3} and when dim(V)=2 and w is in V^{\\otimes 4}. &nbsp\;We also de
 scribe the structure of&nbsp\;TV/(dw) &nbsp\;in these two cases and show t
 hat (most) of them are deformation quantizations of the polynomial ring on
  three variables.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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