Constructing Spectral Triples on C*-Algebras

Joachim Zacharias
University of Glasgow
Wednesday, September 13, 2017 - 11:00

Spectral triples are analogoues of Dirac operators on general  C*-algebras and play a fundamental role in noncommutative geometry.  There are different regularity properties of spectral triples such as  summability and conditions which allow to define a metric on the state  space of the algebra. We will discuss the construction of Dirac  operators with various regularity properties on crossed products and  extensions in the spirit of permanence properties i.e. starting from  triples on the coefficient algebra respectively the ideal and the  quotient we construct a spectral triple on the crossed product  respectively the extension, trying to preserve regularity. This talk  is based on joint work with Andrew Hawkins, and on earlier joint work  with Andrew Hawkins, Stuart White and Adam Skalski.

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