Noncommutative differential geometry on the quantum \(\text{SU}(2)\). I: An algebraic viewpoint

DOI10.1007/BF00533155zbMath0719.46042OpenAlexW1984760906WikidataQ115394992 ScholiaQ115394992MaRDI QIDQ2640110

Junsei Watanabe, Yoshiomi Nakagami, Tetsuya Masuda

Publication date: 1990

Published in: \(K\)-Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00533155

zbMATH Keywords

cyclic homologyHopf algebracoordinate ringquantum algebraic group

Mathematics Subject Classification ID

Related Items (24)

Twisted Homology of Quantum SL(2) - Part II ⋮ A von Neumann algebra framework for the duality of the quantum groups ⋮ Noncommutative differential geometry on the quantum \(\text{SU}(2)\). I: An algebraic viewpoint ⋮ Antisymmetrically deformed quantum homogeneous spaces ⋮ TWISTED ENTIRE CYCLIC COHOMOLOGY, J-L-O COCYCLES AND EQUIVARIANT SPECTRAL TRIPLES ⋮ Logarithmic divergence of heat kernels on some quantum spaces ⋮ On Hopf-cyclic cohomology and Cuntz algebra. ⋮ A characteristic map for compact quantum groups ⋮ Twisted Dirac Operator on Quantum SU(2) in Disc Coordinates ⋮ Hochschild and cyclic homology of quantum groups ⋮ Noncommutative differential geometry on the quantum two sphere of Podlès. I: An algebraic viewpoint ⋮ Fibre product approach to index pairings for the generic Hopf fibration of SU_q(2) ⋮ Le langage des espaces et des groupes quantiques. (The language of quantum spaces and quantum groups) ⋮ Cyclic and Hochschild homology of certain quantum homogeneous spaces ⋮ Complex quantum group, dual algebra and bicovariant differential calculus ⋮ Fredholm modules for quantum Euclidean spheres ⋮ Twisted homology of quantum \(\text{SL}(2)\) ⋮ Twisted Hochschild homology of quantum hyperplanes ⋮ The local index formula for \(\text{SU}_{q}(2)\) ⋮ A locally trivial quantum Hopf fibration. ⋮ Twisted Hochschild homology of quantum flag manifolds: 2-cycles from invariant projections ⋮ The K-theory of the compact quantum group SU_q(2) for q = -1 ⋮ A local index formula for the quantum sphere ⋮ Twisted configurations over quantum Euclidean spheres

Cites Work

• Cyclic homology and the Lie algebra homology of matrices
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Non-commutative differential geometry
• Quantum deformations of certain simple modules over enveloping algebras
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Poisson manifolds and the Schouten bracket
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Noncommutative differential geometry on the quantum \(\text{SU}(2)\). I: An algebraic viewpoint
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