Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces

DOI10.1007/BF00761121zbMath0811.17019OpenAlexW2006450796MaRDI QIDQ1334977

Konrad Schmüdgen, Joachim Apel

Publication date: 26 September 1994

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

Full work available at URL: https://doi.org/10.1007/bf00761121

zbMATH Keywords

quantum spacesnoncommutative differential calculuscovariant first-order differential calculusquantum group \(\text{SL}_ q(2)\)

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Noncommutative topology (46L85) Noncommutative differential geometry (46L87)

Related Items

Quantum Lobachevsky planes ⋮ DERIVATIONS WITH QUANTUM GROUP ACTION ⋮ Commutator representations of differential calculi on the quantum group \(SU_q(2)\) ⋮ JORDANIAN QUANTUM SPHERES ⋮ Field theory on the \(q\)-deformed fuzzy sphere. I. ⋮ Podleś' quantum sphere: dual coalgebra and classification of covariant first-order differential calculus. ⋮ CALCULI, HODGE OPERATORS AND LAPLACIANS ON A QUANTUM HOPF FIBRATION ⋮ HODGE DUALITY OPERATORS ON LEFT-COVARIANT EXTERIOR ALGEBRAS OVER TWO- AND THREE-DIMENSIONAL QUANTUM SPHERES ⋮ On the construction of covariant differential calculi on quantum homogeneous spaces ⋮ Introduction to Quantum Groups ⋮ Quantum spheres for OSpq(1∕2)

Uses Software

• Felix

Cites Work

• Quantum 2-spheres and big q-Jacobi polynomials
• Differential calculus on quantum spheres
• Compact matrix pseudogroups
• Quantum spheres
• Noncommutative differential geometry on the quantum two sphere of Podlès. I: An algebraic viewpoint
• The classification of differential structures on quantum 2-spheres
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Quantum linear groups
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