Algebry operatorów i ich zastosowania w fizyce

We will discuss various lifting properties of C*-algebras. The first part of my talk will be about lifting problems that arise as noncommutative analogues of some topological notions. Namely in topology absolute retracts and absolute neighborhood retracts are, roughly speaking, spaces with good extension properties. Their noncommutative analogues are projective and semiprojective C*-algebras, which are C*-algebras with good lifting properties. Some statements about absolute retracts and neighborhood retracts might be false in the noncommutative setting or hard to prove. We are going to discuss some problems of this sort and their connection with problems in Operator Theory. This part of my talk is almost identical to the talk I gave on January at NCG seminar. This is a joint work with Terry Loring. After that we will discuss some other lifting properties of C*-algebras, for example stability of C*-algeraic relations under small perturbations and property of being RFD (residually finite-dimensional). This will include some other joint work with Loring and a work in progress with Don Hadwin.