Introduction to Quantum Groups

DOI10.1142/S0129055X98000173zbMath0918.17005arXivq-alg/9704002OpenAlexW1990710772WikidataQ56227971 ScholiaQ56227971MaRDI QIDQ4221343

No author found.

Publication date: 17 August 1999

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9704002

zbMATH Keywords

Hopf algebrasquantum groups\(C^*\)-algebrasquantum spherequantum homogeneous spacequantum Lorentz groupHaar functionalco-representationPeter-Weyl theorycompact Hopf *-algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative topology (46L85) Noncommutative differential geometry (46L87) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items

On the monoidal invariance of the cohomological dimension of Hopf algebras, QUANTUM ISOMETRY GROUPS OF SYMMETRIC GROUPS, On actions of compact quantum groups, Quantum automorphism groups and \(\mathrm{SO}(3)\)-deformations, Quantum automorphism groups of finite quantum groups are classical, Quantum \(\mathrm{SO}(3)\) groups and quantum group actions on \(M_{2}\), Twisted product structure and representation theory of the quantum group \(U_q(2)\), The Representation Category of the Quantum Group of a Non-degenerate Bilinear Form, ON QUANTUM SEMIGROUP ACTIONS ON FINITE QUANTUM SPACES

Cites Work

• Quantum orthogonal and symplectic groups and their embedding into quantum GL
• Quantum deformation of Lorentz group
• Compact matrix pseudogroups
• Quantum spheres
• Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
• Some topics on \(GL_ q(n)\)
• New quantum deformation of \(SL(2,\mathbb{C}{})\). Hopf algebra level
• Quantum deformation of classical groups
• Complex quantum groups and their real representations
• Quantum Lorentz group having Gauss decomposition property
• Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces
• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum \(SU(2)\) and \(SO(3)\) groups
• On the classification of quantum Poincaré groups
• The quantum group of a nondegenerate bilinear form.
• Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif. (Quantized enveloping algebras, compact quantum matrix groups and noncommutative differential calculus)
• The Dirac operator and gamma matrices for quantum Minkowski spaces