A twisted spectral triple for quantum \(SU(2)\)

DOI10.1016/j.geomphys.2011.12.019zbMath1245.58004arXiv1109.2326OpenAlexW1507656669MaRDI QIDQ408224

Roger Senior, Jens Kaad

Publication date: 29 March 2012

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.2326

zbMATH Keywords

quantum groupDirac operatorzeta functionspectral dimension\(q\)-deformationspectral triplevon Neumannsemifinite tracelocal Hochschild cocyclequantum SU(2)twisted commutatortwisted trace

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) (K)-theory and homology; cyclic homology and cohomology (19D55) Geometry of quantum groups (58B32) Noncommutative geometry (à la Connes) (58B34) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (12)

Crossed product extensions of spectral triples ⋮ Gauge theory for spectral triples and the unbounded Kasparov product ⋮ Index map, \(\sigma\)-connections, and Connes-Chern character in the setting of twisted spectral triples ⋮ The Podleś spheres converge to the sphere ⋮ On twisting real spectral triples by algebra automorphisms ⋮ Smooth dense subalgebras and Fourier multipliers on compact quantum groups ⋮ A modular spectral triple for \(\kappa\)-Minkowski space ⋮ Heat trace and spectral action on the standard Podleś sphere ⋮ Noncommutative geometry and conformal geometry. III: Vafa-Witten inequality and Poincaré duality ⋮ On the Chern-Gauss-Bonnet theorem and conformally twisted spectral triples for \(C^*\)-dynamical systems ⋮ Non-commutative integration, zeta functions and the Haar state for \(\mathrm{SU}_q(2)\) ⋮ Asymptotic and exact expansions of heat traces

Cites Work

• The Dirac operator on \(\text{SU}_{q}(2)\)
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Equivariant spectral triples on the quantum SU(2) group
• Generalized s-numbers of \(\tau\)-measurable operators
• Differential calculi over quantum groups and twisted cyclic cocycles
• The local index formula in noncommutative geometry
• The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś sphere
• The local index formula in semifinite von Neumann algebras. I: Spectral flow
• The local index formula in semifinite von Neumann algebras. II: the even case
• Twisted homology of quantum \(\text{SL}(2)\)
• Twisted cyclic theory, equivariant KK-theory and KMS states
• The Dirac operator on compact quantum groups
• q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function
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