Symmetric spaces with Jordan structures
Tom 55 / 2002
Streszczenie
In a series of three lectures we give an introduction to symmetric spaces with a certain additional structure: in the first lecture we present examples of interesting structures on symmetric spaces; in particular, generalized conformal structures and the problem of determining their automorphism groups gave rise to the investigation of Jordan structures which are the topic of the following two lectures: we introduce them via the problem of finding a twisted complexification of a symmetric space; the main result to be proved here is that such complexifications correspond bijectively to Jordan extensions of the curvature. Classification shows that, for classical symmetric spaces, there is “generically” one and only one Jordan extension; it is an open and deep problem to find a good conceptual explanation of this fact.
