Two classical results in the quantum mixed case.
Lars Thams (1993)
Journal für die reine und angewandte Mathematik
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Lars Thams (1993)
Journal für die reine und angewandte Mathematik
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H.H. Andersen, P. Polo, Wen Kexin (1991)
Inventiones mathematicae
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H.H. Andersen, P. Polo, K. Wen (1995)
Inventiones mathematicae
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Wasfi A. Hijab (1967)
Journal für die reine und angewandte Mathematik
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R. Budzyński, W. Kondracki (1995)
Banach Center Publications
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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...
K. Schmüdgen (2003)
Banach Center Publications
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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,...
(1997)
Banach Center Publications
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Claus Michael Ringel (1996)
Journal für die reine und angewandte Mathematik
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Wolfgang Rump (2013)
Open Mathematics
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The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated...
Ismael Cohen, Elmar Wagner (2012)
Banach Center Publications
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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...
Vyjayanthi Chari, Andrew Pressley (1991)
Journal für die reine und angewandte Mathematik
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Koornwinder, T.H., Muller, N.M. (1997)
Journal of Lie Theory
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V. Srinivas, L. Barbieri Viale (1994)
Journal für die reine und angewandte Mathematik
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Janusz Grabowski, Giuseppe Marmo (2003)
Banach Center Publications
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Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply properties which are usually additionally required.