Introduction to quantum groups

Abstract

We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum groups and the theory of their actions on compact quantum spaces. We also provide the most important examples, including the classification of quantum SL(2)-groups, their real forms and quantum spheres. We also consider quantum SL_q(N)-groups and quantum Lorentz groups.

very small changes, will appear in Rev. Math. Phys., 46 pages, use commands: csh intro.uu, tex intro (twice)

References in corpus (3)

• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups
• On the classification of quantum Poincaré groups
• The Dirac operator and gamma matrices for quantum Minkowski spaces

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• Phase structures in fuzzy geometries
• On quantum semigroup actions on finite quantum spaces
• Quantum automorphism groups and SO(3)-deformations
• Physical Coordinate as Eigen Values of Translation Operators in Non-commutative Spaces
• Quantum families of maps