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12.The respective G actions were defined in Sec. II.
13.On the level of the algebras the corresponding involutions (denoted by the same letter θ) read, respectively, θ(X) = −X
t, θ(X) = −JX tJ−1, and θ(X, Y) = (−X t, −Y t).
14.Let us recall that the Hermitian structure on endows with a real Riemannian structure - the Fubini-Study metric. Together with ω it makes a Kähler manifold.
15.Orbits of the complexified group play a significant role in quantum information theory. They connect states obtainable via arbitrary local transformations allowed by quantum mechanics, not only unitary ones, supplemented by classical exchange of information between distant laboratories.
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The open dense orbit of B in M × Ω l .
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