The Canonical Complex Structure of Flag Manifolds in a C*-algebra
Chapter
Abstract
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.
Keywords
Homogeneous Space Complex Manifold Grassmann Manifold Flag Manifold Invariant Complex Structure
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