Abstract
An important class of symmetric spaces with twist can be described by Jordan algebras; we call them of the first kind. They can be characterized by the fact that the involution Θ of the conformal group is an inner involution (Th. X1. 1.4) which naturally leads to the Jordan inverse of a Jordan algebra (Prop. X1.1.5). Specializing the Peirce-theory from Section X.5 to this case, we define a real Cayley transform which in many cases yields generalized tube domain realizations (Th. XI.2.8) which are useful in the study of certain causal symmetric spaces (Section 3).
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© 2000 Springer-Verlag Berlin Heidelberg
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(2000). Chapter XI: Spaces of the first and of the second kind. In: Bertram, W. (eds) The Geometry of Jordan and Lie Structures. Lecture Notes in Mathematics, vol 1754. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44458-0_11
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DOI: https://doi.org/10.1007/3-540-44458-0_11
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Publisher Name: Springer, Berlin, Heidelberg
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