A noncommutative 2-sphere generated by the quantum complex plane

Ismael Cohen; Elmar Wagner

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Displaying similar documents to “A noncommutative 2-sphere generated by the quantum complex plane”

When is a quantum space not a group?

Piotr Mikołaj Sołtan (2010)

Banach Center Publications

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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...

Contractible quantum Arens-Michael algebras

Nina V. Volosova (2010)

Banach Center Publications

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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,...

Quantum spaces: notes and comments on a lecture by S. L. Woronowicz

R. Budzyński, W. Kondracki (1995)

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Commutator representations of covariant differential calculi

K. Schmüdgen (2003)

Banach Center Publications

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An introduction to quantum annealing

Diego de Falco, Dario Tamascelli (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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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...

The quantum spheres and their embedding into quantum Minkowski space-time.

Lagraa, M. (2002)

Journal of Applied Mathematics

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An introduction to quantum annealing

Diego de Falco, Dario Tamascelli (2011)

RAIRO - Theoretical Informatics and Applications

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On quantum vector fields in general relativistic quantum mechanics.

Janys̆ka, Joseph, Modugno, Marco (1997)

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On the quantum groups and semigroups of maps between noncommutative spaces

Maysam Maysami Sadr (2017)

Czechoslovak Mathematical Journal

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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...