Abstract
In this chapter we will discuss the notion of a “dynamical correspondence”, which is applicable in both JB and JBW contexts. This generalizes the correspondence of observables and generators of one-parameter groups of automorphisms in quantum mechanics. It is closely related to Connes’ concept of orientation [36, Definition 4.11] that he used as a key property in his characterization of the natural self-dual cones associated with von Neumann algebras (i.e., the cones P ♮ξ of Tomita—Takesaki theory). Both can be thought of as ways to specify possible Lie structures compatible with a given Jordan structure.
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© 2003 Springer Science+Business Media New York
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Alfsen, E.M., Shultz, F.W. (2003). Dynamical Correspondences. In: Geometry of State Spaces of Operator Algebras. Mathematics: Theory & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0019-2_6
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DOI: https://doi.org/10.1007/978-1-4612-0019-2_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6575-7
Online ISBN: 978-1-4612-0019-2
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