Related papers: Embeddable Quantum Homogeneous Spaces
There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…
We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so…
We consider homogeneous spaces of Lie groups with compact stabilizer subgroups of two types: those with integrable invariant distributions and those with geodesic orbit invariant Riemannian metrics. The latter means that for an arbitrary…
We introduce the notion of integrable modules over $\imath$quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we prove that each integrable module over a quantum group is…
We introduce a non commutative analog of the Bohr compactification. Starting from a general quantum group G we define a compact quantum group bG which has a universal property such as the universal property of the classical Bohr…
In this article, we give a definition for measured quantum groupoids. We want to get objects with duality extending both quantum groups and groupoids. We base ourselves on J. Kustermans and S. Vaes' works about locally compact quantum…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
We study equivariant affine embeddings of homogeneous spaces and their equivariant automorphisms. An example of a quasiaffine, but not affine, homogeneous space with finitely many equivariant automorphisms is presented. We prove the…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
We discuss the liberation question, in the homogeneous space setting. Our first series of results concerns the axiomatization and classification of the families of compact quantum groups $G=(G_N)$ which are "uniform", in a suitable sense.…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
We introduce a class of automorphisms of compact quantum groups which may be thought of as inner automorphisms and explore the behaviour of normal subgroups of compact quantum groups under these automorphisms. We also define the notion of…
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…
Bornological quantum groups were introduced by Voigt in order to generalize the theory of algebraic quantum groups in the sense of van Daele. In particular the class of bornological quantum groups contains all classical locally compact…
We introduce the notion of self-similarity for compact quantum groups. For a finite set $X$, we introduce a $C^*$-algebra $\mathbb{A}_X$, which is the quantum automorphism group of the infinite homogeneous rooted tree $X^*$. Self-similar…
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under…
This paper presents a formulation of the notion of monotonicity on homogeneous spaces. We review the general theory of invariant cone fields on homogeneous spaces and provide a list of examples involving spaces that arise in applications in…