arXiv 0902.37772009-02-23math.QAmath.KT

Fibre product approach to index pairings for the generic Hopf fibration of SU_q(2)

Elmar Wagner

备注：: 15 pages

英文摘要：

A fibre product construction is used to give a description of quantum line bundles over the generic Podles spheres by gluing two quantum discs along their boundaries. Representatives of the corresponding $K_0$-classes are given in terms of 1-dimensional projections belonging to the C*-algebra, and in terms of analogues of the classical Bott projections. The $K_0$-classes of quantum line bundles derived from the generic Hopf fibration of quantum SU(2) are determined and the index pairing is computed. It is argued that taking the projections obtained from the fibre product construction yields a significant simplification of earlier index computations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SUq(2) over all Podles spheres and with a locally trivial Hopf fibration of S^3_{pq}. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SUq(2) and S^3_{pq}. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them.

2003-02-20math.KTmath.QA

Yang-Mills-Scalar-Matter Fields in the Quantum Hopf Fibration

In this paper we present solutions to the non-commutative geometrical version of the Yang-Mills-Scalar-Matter theory in the Hopf fibration using the $3D$--calculus.

2022-04-30math.QA

Toeplitz algebras in quantum Hopf fibrations

The paper presents applications of Toeplitz algebras in Noncommutative Geometry. As an example, a quantum Hopf fibration is given by gluing trivial U(1) bundles over quantum discs (or, synonymously, Toeplitz algebras) along their boundaries. The construction yields associated quantum line bundles over the generic Podles spheres which are isomorphic to those from the well-known Hopf fibration of quantum SU(2). The relation between these two versions of quantum Hopf fibrations is made precise by giving an isomorphism in the category of right U(1)-comodules and left modules over the C*-algebra of…

2018-02-16math.QA

Hopf fibration and monopole connection over the contact quantum spheres

Noncommutative geometry of quantised contact spheres introduced by Omori, Maeda, Miyazaki and Yoshioka is studied. In particular it is proven that these spheres form a noncommutative Hopf fibration in the sense of Hopf-Galois extensions. The monopole (strong) connection is constructed, and projectors describing projective modules of all monopole charges are computed.

2003-01-13math-phmath.MPmath.QA

A Locally Trivial Quantum Hopf Fibration

The irreducible *-representations of the polynomial algebra O(S^3_{pq}) of the quantum 3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal C*-algebra are shown to coincide with their classical counterparts. The U(1)-action on O(S^3_{pq}) corresponding for p=1=q to the classical Hopf fibration is proven to be Galois (free). The thus obtained locally trivial Hopf-Galois extension is shown to be relatively projective (admitting a strong connection) and non-cleft. The latter is proven by determining an appropriate Chern-Connes pairing.

2002-09-26math.OAmath.QA

On the Relationship between Classical and Deformed Hopf Fibrations

The $θ$-deformed Hopf fibration $\mathbb{S}^3_θ\to \mathbb{S}^2$ over the commutative $2$-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. The latter isomorphism is equivariant under an appropriate notion of infinitesimal gauge transformations in these contexts. Gauge transformations and connections on associated modules are studied and are shown to be sensitive to the deformation parameter. A homotopy theore…

2020-02-23hep-thmath-phmath.MP

更多相关论文收起更多论文

Deformation Quantization of Symplectic Fibrations

A symplectic fibration is a fibre bundle in the symplectic category. We find the relation between deformation quantization of the base and the fibre, and the total space. We use the weak coupling form of Guillemin, Lerman, Sternberg and find the characteristic class of deformation of symplectic fibration. We also prove that the classical moment map could be quantized if there exists an equivariant connection. Along the way we touch upon the general question of quantization with values in a bundle of algebras. We consider Fedosov's construction of deformation quantization in general. In the App…

1998-02-16math.DGmath.QA

Calculi, Hodge operators and Laplacians on a quantum Hopf fibration

We describe Laplacian operators on the quantum group SUq (2) equipped with the four dimensional bicovariant differential calculus of Woronowicz as well as on the quantum homogeneous space S2q with the restricted left covariant three dimensional differential calculus. This is done by giving a family of Hodge dualities on both the exterior algebras of SUq (2) and S2q . We also study gauged Laplacian operators acting on sections of line bundles over the quantum sphere.

2012-10-03hep-thmath-phmath.MP

纤维函子与Hopf代数的重构

Fibre functors and reconstruction of Hopf algebras

本文提出Tannaka-Krein型重构定理，证明当张量范畴具有相容的monoidal模范畴结构时，可通过相对coend重构辫子Hopf代数，并应用于对数Kazhdan-Lusztig猜想。

2024-05-16math.CTmath.QA

Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration $S^7 \to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equatio…

2012-09-07math-phmath.MPmath.QA

Quantum Homogeneous Spaces and Coalgebra Bundles

It is shown that quantum homogeneous spaces of a quantum group H can be viewed as fibres of quantum fibrations with the total space H that are dual to coalgebra bundles. As concrete examples of such structures the fibrations with the quantum 2-sphere and the quantum hyperboloid fibres are considered.

1997-04-19math-phmath.MPmath.QA