Structure and applications of real 𝐶*-algebras
Jonathan Rosenberg · Contemporary mathematics - American Mathematical Society · 2016
For a long time, practitioners of the art of operator algebras always worked over the complex numbers, and nobody paid much attention to real C ∗ C^* -algebras. Over the last thirty years, that situation has changed, and it’s become apparent that real C ∗ C^* -algebras have a lot of extra structure not evident from their complexifications. At the same time, interest in real C ∗ C^* -algebras has been driven by a number of compelling applications, for example in the classification of manifolds of positive scalar curvature , in representation theory , and in the study of orientifold string theories . We will discuss a number of interesting examples of these, and how the real Baum-Connes conjecture plays an important role.