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Introduits dans les années 80 pour mettre sous une forme mathématique certaines notions de physique théorique, les groupes quantiques ont conquis une place prépondérante au sein des mathématiques grâce à des liens étroits avec de nombreux autres domaines, comme la théorie des noeuds, les fonctions spéciales ou les représentations des groupes finis.

Quantum groups. --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory --- Groupes quantiques

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Topological groups. Lie groups --- 51 <082.1> --- Mathematics--Series --- Quantum groups. --- Groupes quantiques. --- Quantum groups --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory

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Ordered algebraic structures --- 51 <082.1> --- Mathematics--Series --- Hopf algebras --- Quantum groups --- Groupes quantiques --- Hopf, Algèbres de --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory --- Algebras, Hopf --- Algebraic topology --- Groupes quantiques. --- Hopf, Algèbres de.

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This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an activity at the Max-Planck-Institute for Mathematics in Bonn. Contributions byTomasz Brzezinski, Branimir Cacic, Rita Fioresi, Rita Fioresi and Fabio Gavarini, Debashish Goswami, Christian Kassel, Avijit Mukherjee, Alfons Van Daele, Robert Wisbauer, Alessandro Zampini The volume is aimed as introducing techniques and results on Quantum Groups and Noncommutative Geometry, in a form that is accessible to other researchers in related areas as well as to advanced graduate students. The topics covered are of interest to both mathematicians and theoretical physicists. Prof. Dr. Matilde Marcolli, Department of Mathematics, California Institute of Technology, Pasadena, California, USA. Dr. Deepak Parashar, Cambridge Cancer Trials Centre and MRC Biostatistics Unit, University of Cambridge, United Kingdom.

Electronic books. -- local. --- Noncommutative differential geometry. --- Quantum groups. --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Mathematical Theory --- Mathematics. --- Geometry. --- Differential geometry, Noncommutative --- Geometry, Noncommutative differential --- Non-commutative differential geometry --- Infinite-dimensional manifolds --- Operator algebras --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory --- Euclid's Elements

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Quantum groups --- 517.986 --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Topological algebras. Theory of infinite-dimensional representations --- Quantum theory --- Théorie des groupes --- Théorie quantique