Seminario di algebra e geometria
ore
11:45
presso - Aula Da Stabilire -
I will explain how the graph C*-algebras of a trimmable graph
can be decomposed as U(1)-equivariant pullback of two simpler
C*-algebras. A main example is given by the algebra of Vaksman-Soibelman
quantum sphere, that can be realized as pushout of a lower dimensional
quantum sphere and the product of a quantum ball with a circle (we
understand the pullback of C*-algebras as pushout of the underlying
"noncommutative spaces"). The U(1)-invariant part of this pullback
diagram gives a "CW complex" realization of quantum projective spaces
that allows to give an explicit description of the K-theory generators.
Further examples include quantum lens spaces, one-loop extensions of
Cuntz algebras of the Toeplitz algebra. This is a joint work with
Francesca Arici, Piotr M. Hajac and Mariusz Tobolski.