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SUMMARY:Daniel Nakano (University of Georgia\, USA)
DTSTART:20210222T150000Z
DTEND:20210222T160000Z
DTSTAMP:20260422T180300Z
UID:QGS/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/11/">Non
 commutative Tensor Triangular Geometry</a>\nby Daniel Nakano (University o
 f Georgia\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn
  this talk\, I will show how to develop a general noncommutative version o
 f Balmer's tensor triangular geometry that is applicable to arbitrary mono
 idal triangulated categories (M$\\Delta$C). Insights from noncommutative r
 ing theory is used to obtain a framework for prime\, semiprime\, and compl
 etely prime (thick) ideals of an M$\\Delta$C\, $\\mathbf K $\, and then to
  associate to $\\mathbf K$ a topological space --the Balmer spectrum $\\te
 xt{Spc }{\\mathbf K}$.\n\nWe develop a general framework for (noncommutati
 ve) support data\, coming in three different flavors\, and show that $\\te
 xt{Spc }{\\mathbf K}$ is a universal terminal object for the first two not
 ions (support and weak support). The first two types of support data are t
 hen used in a theorem that gives a method for the explicit classification 
 of the thick (two-sided) ideals and the Balmer spectrum of an M$\\Delta$C.
  The third type (quasi support) is used in another theorem that provides a
  method for the explicit classification of the thick right ideals of $\\ma
 thbf K$\, which in turn can be applied to classify the thick two-sided ide
 als and $\\text{Spc }{\\mathbf K}$.\n\nIf time permits applications will b
 e given for quantum groups and non-cocommutative finite-dimensional Hopf a
 lgebras studied by Benson and Witherspoon.\n\nThis is joint and ongoing wo
 rk with Milen Yakimov and Kent Vashaw\n
LOCATION:https://researchseminars.org/talk/QGS/11/
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