Introduction to Prehomogeneous Vector
                    Spaces

Kimura, Tatsuo

doi:10.1090/mmono/215

Cited by 72 publications

(108 citation statements)

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“…The matrix M − (Q) is the (opposite of the) pseudo-Euclidean metric of a noncompact, non-Riemannian rigid special Kähler manifold related to the duality orbit of the black hole electromagnetic charges (to which Q belongs), which is an example of pre-homogeneous vector space (PVS) 23 . In turn, the nature of the rigid special manifold may be Kähler or pseudo-Kähler, depending on the existence of a U (1) or SO(1, 1) connection b .…”

Section: Duality Orbits Rigid Special Kähler Geometry and Pre-homogementioning

confidence: 99%

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Freudenthal duality and black holes: From groups of type E₇ to pre-homogeneous spaces

Marrani¹

2017

The Fourteenth Marcel Grossmann Meeting

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Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. It was introduced in four-dimensional Maxwell-Einstein theories coupled to a non-linear sigma model of scalar fields.In this short review, I will consider its relation to the U -duality Lie groups of type E 7 in extended supergravity theories, and comment on the relation between the Hessian of the black hole entropy and the pseudo-Euclidean, rigid special (pseudo)Kähler metric of the pre-homogeneous spaces associated to the U -orbits.

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Section: Duality Orbits Rigid Special Kähler Geometry and Pre-homogementioning

confidence: 99%

“…For more details, see e.g. 23,[25][26][27] . Amazingly, simple, non-degenerate groups of type E 7 (relevant to D = 4 Einstein (super)gravities with symmetric scalar manifolds) almost saturate the list of irreducible PVS with unique G-invariant polynomial of degree 4 ( 25 ; also cfr.…”

Section: Duality Orbits Rigid Special Kähler Geometry and Pre-homogementioning

confidence: 99%

Freudenthal duality and black holes: From groups of type E₇ to pre-homogeneous spaces

Marrani¹

2017

The Fourteenth Marcel Grossmann Meeting

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“…The system has only one relative invariant under the action of the SLOCC group which is an analougus quantity to the three-tangle for three qubits. This property is due to the fact that the system is a so called prehomogeneous vector space [13,14]. Three fermions with seven or eight single particle states also form a prehomogeneous vector space with a single SLOCC invariant, however, in the case of nine single particle states there are already four independent continous SLOCC invariants [16] and the physical meaning of these ones is not so clear yet.…”

Section: Arxiv:14086735v1 [Quant-ph] 28 Aug 2014mentioning

confidence: 99%

Coffman-Kundu-Wootters inequality for fermions

Sárosi

Lévay

2014

Phys. Rev. A

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We derive an inequality for three fermions with six single particle states which reduces to the sum of the famous Coffman-Kundu-Wootters inequalities when an embedded three qubit system is considered. We identify the quantities which are playing the role of the concurrence, the threetangle and the invariant det ρA + det ρB + det ρC for this tripartite system. We show that this latter one is almost interchangeable with the von Neumann entropy and conjecture that it measures the entanglement of one fermion with the rest of the system. We prove that the vanishing of the fermionic "concurrence" implies that the two particle reduced density matrix is a mixture of separable states. Also the vanishing of this quantitiy is only possible in the GHZ class, where some genuie tripartite entanglement is present and in the separable class. Based on this we conjecture that this "concurrence" measures the amount of entanglement between pairs of fermions. We identify the well-known "spin-flipped" density matrix in the fermionic context as the reduced density matrix of a special particle-hole dual state. We show that in general this dual state is always canonically defined by the Hermitian inner product of the fermionic Fock space and that it can be used to calculate SLOCC covariants. We show that Fierz identities known from the theory of spinors relate SLOCC covariants with reduced density matrix elements of the state and its "spin-flipped" dual. CONTENTS

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“…Lorsque z est nul, l'algèbre g est préhomogène si et seulement si G a une orbite coadjointe ouverte, c'est-à-dire si g * est une espace préhomogène pour G au sens de Kimura-Sato (voir [Kim03]). C'est pourquoi nous avons choisi cette terminologie.…”

Section: Définitionsunclassified

Algèbres de Lie quasi-réductives

Duflo

Khalgui

Torasso

2012

Transformation Groups

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Introduction to Prehomogeneous Vector Spaces

Cited by 72 publications

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Freudenthal duality and black holes: From groups of type E₇ to pre-homogeneous spaces

Freudenthal duality and black holes: From groups of type E₇ to pre-homogeneous spaces

Coffman-Kundu-Wootters inequality for fermions

Algèbres de Lie quasi-réductives

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Introduction to Prehomogeneous Vector Spaces

Cited by 72 publications

References 0 publications

Freudenthal duality and black holes: From groups of type E7 to pre-homogeneous spaces

Freudenthal duality and black holes: From groups of type E7 to pre-homogeneous spaces

Coffman-Kundu-Wootters inequality for fermions

Algèbres de Lie quasi-réductives

Contact Info

Product

Resources

About

Freudenthal duality and black holes: From groups of type E₇ to pre-homogeneous spaces

Freudenthal duality and black holes: From groups of type E₇ to pre-homogeneous spaces