The Canonical Complex Structure of Flag Manifolds in a C*-algebra

The final objective of this article is to study the space of increasing n -tuples of self-adjoint idempotents in a C *-algebra—which is called a flag manifold—from a differential geometric point of view. It is proved that a flag manifold has a natural intrinsic complex structure. Some properties of this structure are examined and a generalization of the well-known Gram-Schmidt construction is considered. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.