Titlebook: Quantum Groups and Their Representations; Anatoli Klimyk,Konrad Schmüdgen Book 1997 Springer-Verlag Berlin Heidelberg 1997 Vector space.al

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Corepresentation Theory and Compact Quantum Groupste two classes of Hopf algebras resp. Hopf ?-algebras, called cosemisimple Hopf algebras resp. compact quantum group algebras, which are determined by their irreducible resp. unitary corepresentations. The second class leads at once to Woronowicz’ compact quantum group .*-algebras studied in Sect. 1

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Covariant Differential Calculus on Quantum Spaces of relativity and others. There are various physical ideas and considerations (quantum gravity, discrete space-time structures, models of elementary particle physics) that strongly motivate the replacement of the commutative algebra of .-functions on a manifold by an appropriate noncommutative alge

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Corepresentation Theory and Compact Quantum Groups their irreducible resp. unitary corepresentations. The second class leads at once to Woronowicz’ compact quantum group .*-algebras studied in Sect. 11.4. In Sect. 11.5 the irreducible representations of the quantum group .(N) when . is not a root of unity are classified. The final Sect. 11.6 gives an introduction to, quantum homogeneous spaces.

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1864-5879 inner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. .The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized alg

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Quasitriangularity and Universal ,-Matricesr is devoted to a detailed study of these topics. The universal R-matrices, the .-matrices and the main .-functionals for the vector representations of Drinfeld-Jimbo algebras are explicitly determined.

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