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.