Dirac Operators on Quantum Projective Spaces

Abstract

We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant even spectral triples. If l is odd and N=(l+1)/2, the spectral triple is real with KO-dimension 2l mod 8.

54 pages, no figures, dcpic, pdflatex

References in corpus (7)

• Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
• The Noncommutative Geometry of the Quantum Projective Plane
• A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
• The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
• Dirac operators on all Podles quantum spheres
• The local index formula for quantum SU(2)
• Dirac Operators on Quantum Flag Manifolds

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• Heat trace and spectral action on the standard Podles sphere
• Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds
• Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
• The Parthasarathy formula and a spectral triple for the quantum Lagrangian Grassmannian of rank two
• Quantum Dimension and Quantum Projective Spaces
• Differential Calculi on Quantum Principal Bundles over Projective Bases
• Dolbeault-Dirac operators, quantum Clifford algebras and the Parthasarathy formula
• Topics in Noncommutative Geometry
• Spectral triples on the Jiang-Su algebra
• On PBW-deformations of braided exterior algebras
• A Hodge - De Rham Dirac operator on the quantum $\mathrm{SU}(2)$
• Quantum Riemannian geometry of quantum projective spaces
• Cubic Dirac operator for $U_q({\mathfrak{sl}}_2)$
• Fubini-Study metrics and Levi-Civita connections on quantum projective spaces
• Twisted sigma-model solitons on the quantum projective line