### PBW and duality theorems for quantum groups and quantum current algebras.

Enriquez, Benjamin (2003)

Journal of Lie Theory

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Enriquez, Benjamin (2003)

Journal of Lie Theory

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Zhang, Shouchuan, Gould, Mark D., Zhang, Yao-Zhong (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Gabriella Böhm, Kornél Szlachányi (1997)

Banach Center Publications

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By allowing the coproduct to be non-unital and weakening the counit and antipode axioms of a C*-Hopf algebra too, we obtain a selfdual set of axioms describing a coassociative quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. It is the same structure that can be obtained by replacing the multiplicative unitary of Baaj and Skandalis with a partial isometry. The algebraic properties, the existence...

Sergio Albeverio, Bakhrom A. Omirov, Isamiddin S. Rakhimov (2006)

Extracta Mathematicae

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Jerzy Białkowski (2004)

Open Mathematics

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Kadison, Lars, Stolin, A.A. (2001)

Beiträge zur Algebra und Geometrie

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Flaut, Cristina (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Hübner, Marion, Petersson, Holger P. (2004)

Beiträge zur Algebra und Geometrie

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Dieterich, Ernst (2000)

AMA. Algebra Montpellier Announcements [electronic only]

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Kuniba, Atsuo, Nakanishi, Tomoki, Suzuki, Junji (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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J. Monk (1993)

Banach Center Publications

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Julian Ławrynowicz, Jakub Rembieliński, Francesco Succi (1996)

Banach Center Publications

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The notion of a ${J}^{3}$-triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements....