TY - JOUR
T1 - A characterization of symmetric tube domains by convexity of Cayley transform images
AU - Kai, Chifune
AU - Nomura, Takaaki
N1 - Funding Information:
This research was partially supported by Grant-in-Aid for Scientific Research (No. 14340044), Japan Society for the Promotion of Science.
PY - 2005/7
Y1 - 2005/7
N2 - In this paper, we show that a homogeneous tube domain is symmetric if and only if its Cayley transform image as well as the dual Cayley transform image of the dual tube domain is convex. In this case, the parameters of these Cayley transforms reduce to specific ones, so that they are essentially the usual Cayley transforms defined in terms of Jordan algebra structure.
AB - In this paper, we show that a homogeneous tube domain is symmetric if and only if its Cayley transform image as well as the dual Cayley transform image of the dual tube domain is convex. In this case, the parameters of these Cayley transforms reduce to specific ones, so that they are essentially the usual Cayley transforms defined in terms of Jordan algebra structure.
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U2 - 10.1016/j.difgeo.2005.03.004
DO - 10.1016/j.difgeo.2005.03.004
M3 - Article
AN - SCOPUS:20544447457
SN - 0926-2245
VL - 23
SP - 38
EP - 54
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
IS - 1
ER -