The projectivity of C^*-algebras and the topology of their spectra

Zynaida Lykova (Newcastle University)

Tuesday 11th November, 2014 16:00-17:00 Maths 416


In  this talk we investigate left projectivity of C^*-algebras which are not necessary commutative. 
A complete description of left projective  commutative C^*-algebras C_0(\Omega) as algebras 
having a  paracompact spectrum \Omega was given by Helemskii in 1970. 
However, it is quite difficult to get a  complete description of left projective noncommutative C^*-algebras 
because of the richness of   C^*-algebras. On the other hand, very broad classes of C^*-algebras can be 
obtained as  C^*-algebras defined by continuous fields of very simple C^*-algebras.   We give necessary  
and sufficient conditions for the left projectivity and biprojectivity of (Banach)  C^*-algebras defined by 
locally trivial continuous fields of (Banach)  C^*-algebras. 

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