**
Journal of Lie Theory**

8(1), 139-152 (1998)

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Complex Structures contained in classical groups

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C. Birkenhake

Christina Birkenhake

Mathematisches Institut

Bismarckstr. 1 1/2

D-91054 Erlangen

birkenhake@mi.uni-erlangen.de

**Abstract:** For any classical group $\scriptstyle G$ let $\scriptstyle \cc(G) = \{J \in G \, | \, J^2 = -\1 \}$ denote the space of complex structures in $\scriptstyle G$.\, $\scriptstyle \cc(G)$ is a symmetric space with finitely many connected components, which are described explicitly. In particular these components are flag domains in the sense of J. A. Wolf. Moreover it is shown that the components of $\scriptstyle\cc(G)$ are parameter spaces for nondegenerate complex tori with certain endomorphism structure.

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