Differenzierbare G-Mannigfaltigkeiten

Jänich, Klaus

doi:10.1007/bfb0098472

Cited by 45 publications

(18 citation statements)

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“…There are also many other remarkable results, especially for actions of compact groups (see, e.g., [51,Chap. IV], [62]), but, to the best of our knowledge, no complete explicit classifications beyond group dimension (n − 1)(n − 2)/2 + 2, with n ≥ 6, have been found.…”

Section: Remark 34mentioning

confidence: 96%

Proper actions of high-dimensional groups on complex manifolds

Isaev

2015

Bull. Math. Sci.

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Proper group actions are ubiquitous in mathematics and have many of the attractive features of actions of compact groups. In this survey, we discuss proper actions of Lie groups on smooth manifolds. If the group dimension is sufficiently high, all proper effective actions can be explicitly determined, and our principal goal is to provide a comprehensive exposition of known classification results in the complex setting. They include a complete description of Kobayashi-hyperbolic manifolds with high-dimensional automorphism group, which is a case of special interest.

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Section: Remark 34mentioning

confidence: 96%

Proper actions of high-dimensional groups on complex manifolds

Isaev

2015

Bull. Math. Sci.

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“…we have to show that the estimation schemeÊ N defined in Equation (20) satisfies the LDP with rate functionÎ given in (26). The first step is to check thatÎ is well defined.…”

Section: Proof Of Theorem 32mentioning

confidence: 99%

Quantum State Estimation and Large Deviations

Keyl¹

2006

Rev. Math. Phys.

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In this paper we propose a method to estimate the density matrix ρ of a d-level quantum system by measurements on the N -fold system in the joint state ρ ⊗N . The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning pure states and the estimation of the spectrum of ρ. We show that it is consistent (i.e. the original input state ρ is recovered with certainty if N → ∞), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N → ∞. Finally we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.

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“…To prove parts (ii) and (vii) we first look closely at Mann's result, particularly his use of a theorem due to Borel which may be found in [1]. In parts (ii) and (vii) we will show that the tangent spaces to K~/H1 and 1£2/1t2 are orthogonal at 0, thus the inner product in To(M) arising from the Riemannian metric on M will be realized as the product of the invariant inner products on To(K1/H1) and To(K2/H2).…”

Section: Classification Theorem Let M = K/h Be An M-dimensional Compmentioning

confidence: 99%

Compact homogeneous Riemannian manifolds

Lukesh

1978

Geom Dedicata

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Differenzierbare G-Mannigfaltigkeiten

Cited by 45 publications

References 0 publications

Proper actions of high-dimensional groups on complex manifolds

Proper actions of high-dimensional groups on complex manifolds

Quantum State Estimation and Large Deviations

Compact homogeneous Riemannian manifolds

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