Displaying similar documents to “Equivariant Morita equivalences between Podleś spheres”

Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres

Elmar Wagner (2011)

Banach Center Publications

Similarity:

It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2)...

Dirac operator on the standard Podleś quantum sphere

Ludwik Dąbrowski, Andrzej Sitarz (2003)

Banach Center Publications

Similarity:

Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podleś quantum sphere: equivariant representation, chiral grading γ, reality structure J and the Dirac operator D, which has bounded commutators with the elements of the algebra and satisfies the first order condition.

The garden of quantum spheres

Ludwik Dąbrowski (2003)

Banach Center Publications

Similarity:

A list of known quantum spheres of dimension one, two and three is presented.

Quantum-classical interactions and galois type extensions

Władysław Marcinek (2003)

Banach Center Publications

Similarity:

An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model...

On the quantum groups and semigroups of maps between noncommutative spaces

Maysam Maysami Sadr (2017)

Czechoslovak Mathematical Journal

Similarity:

We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. Sołtan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC...

When is a quantum space not a group?

Piotr Mikołaj Sołtan (2010)

Banach Center Publications

Similarity:

We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of C*-algebras) do not admit any quantum group structure. We also provide a number of examples which include some very well known quantum spaces. Our tools include several purely quantum group theoretical results as well as study of existence of characters and traces on C*-algebras describing the considered quantum spaces as well as...

Problems in the theory of quantum groups

Shuzhou Wang (1997)

Banach Center Publications

Similarity:

This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.

A noncommutative 2-sphere generated by the quantum complex plane

Ismael Cohen, Elmar Wagner (2012)

Banach Center Publications

Similarity:

S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous...

Index pairings for pullbacks of C*-algebras

Ludwik Dąbrowski, Tom Hadfield, Piotr M. Hajac, Rainer Matthes, Elmar Wagner (2012)

Banach Center Publications

Similarity:

In this overview, we study how to reduce the index pairing for a fibre-product C*-algebra to the index pairing for the C*-algebra over which the fibre product is taken. As an example we analyze the case of suspensions and apply it to noncommutative instanton bundles of arbitrary charges over the suspension of quantum deformations of the 3-sphere.

An introduction to quantum annealing

Diego de Falco, Dario Tamascelli (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum...

Contractible quantum Arens-Michael algebras

Nina V. Volosova (2010)

Banach Center Publications

Similarity:

We consider quantum analogues of locally convex spaces in terms of the non-coordinate approach. We introduce the notions of a quantum Arens-Michael algebra and a quantum polynormed module, and also quantum versions of projectivity and contractibility. We prove that a quantum Arens-Michael algebra is contractible if and only if it is completely isomorphic to a Cartesian product of full matrix C*-algebras. Similar results in the framework of traditional (non-quantum) approach are established,...

Half-liberated real spheres and their subspaces

Julien Bichon (2016)

Colloquium Mathematicae

Similarity:

We describe the quantum subspaces of Banica-Goswami's half-liberated real spheres, showing in particular that there is a bijection between the symmetric ones and the conjugation stable closed subspaces of the complex projective spaces.