scientific article; zbMATH DE number 4188043
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Publication:5752725
zbMath0721.17014MaRDI QIDQ5752725
Publication date: 1991
Full work available at URL: http://www.numdam.org/item?id=CM_1991__77_2_199_0
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representationscompact quantum groupsVerma modulesstar operationcompact matrix pseudogrouptype I \(C^ *\)-algebra
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Noncommutative topology (46L85) Noncommutative differential geometry (46L87) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)
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Quantum homogeneous spaces, duality and quantum 2-spheres ⋮ The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function ⋮ Free products of compact quantum groups ⋮ Hilbert space representations of cross product algebras. II. ⋮ Deformations of compact quantum groups via Rieffel's quantization ⋮ Hunt's formula for SU_q(N) and U_q(N) ⋮ Maximum modulus principle for ``holomorphic functions on the quantum matrix ball ⋮ SU q (3) corepresentations and bivariate q-Krawtchouk polynomials ⋮ The field of quantum \(\mathrm{GL}(N,\mathbb {C})\) in the \(\mathrm C^*\)-algebraic setting ⋮ Compact quantum groups and groupoid \(C^*\)-algebras ⋮ Twisted product structure and representation theory of the quantum group \(U_q(2)\) ⋮ Coalgebras Over the Higher Rank Symplectic Groups ⋮ On the classification of compact quantum groups \(U_{\theta}(2)\) ⋮ Locally compact quantum groups ⋮ Quantum dressing orbits on compact groups ⋮ Woronowicz construction of compact quantum groups for functions on permutations. classification result for \(N=3\) ⋮ Representations and classification of the compact quantum groups Uq(2) for complex deformation parameters ⋮ Quantum groups with projection and extensions of locally compact quantum groups ⋮ Coactions of Hopf algebras on Cuntz algebras and their fixed point algebras ⋮ Primitive ideals of \({\mathbf C}_ q[SL(3)\)]
Cites Work
- An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
- The twisted SU(3) group. Irreducible *-representations of the \(C^*\)-algebra \(C(S_{\mu}U(3))\)
- A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
- Compact matrix pseudogroups
- Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
- Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
- A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\)
- Algebra of functions on the quantum group SU(2)
- Introduction to Lie Algebras and Representation Theory
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