Geometric foundations for classical $\mathrm{U}(1)$-gauge theory on noncommutative manifolds

DOI10.1007/S00220-024-05038-YMaRDI QIDQ6593163

Publication date: 26 August 2024

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

Noncommutative differential geometry (46L87) Partial differential equations on manifolds; differential operators (58Jxx) Infinite-dimensional manifolds (58Bxx)

Cites Work

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Coherence for categories with group structure: An alternative approach
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Kohaerenz in Kategorien mit Gruppenstruktur
The classification of differential structures on quantum 2-spheres
Stable isomorphism and strong Morita equivalence of $C^*$-algebras
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Braided tensor categories
Circle actions on $C^*$-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence
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Lifting spectral triples to noncommutative principal bundles
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Gauge theory on noncommutative Riemannian principal bundles
Remarks on anomalous symmetries of $C^*$-algebras
Unbounded bivariant $K$-theory and correspondences in noncommutative geometry
Strong connections on quantum principal bundles
Spectral flow and the unbounded Kasparov product
Line bundles and the Thom construction in noncommutative geometry
Einstein manifolds
Quadratic functions in geometry, topology, and $M$-theory
A local index formula for the quantum sphere
T-duality simplifies bulk-boundary correspondence
$T$-duality for principal torus bundles and dimensionally reduced Gysin sequences
$C^*$-algebras associated with real multiplication
Laplacians and gauged Laplacians on a quantum Hopf bundle
Pimsner Algebras and Circle Bundles
Twisted cyclic theory, equivariant KK-theory and KMS states
The graded ring of quantum theta functions for noncommutative torus with real multiplication
Projective Modules over Higher-Dimensional Non-Commutative Tori
Morita equivalence for crossed products by Hilbert $C^\ast $-bimodules
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Noncommutative Cosmology
ON GRADED -ALGEBRAS
Quadratic Irrationals
Dynamics of compact quantum metric spaces
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Quantum Riemannian Geometry
Tensor Categories
Quantum groups, differential calculi and the eigenvalues of the Laplacian
Holomorphic Structures on the Quantum Projective Line
On isomorphisms of algebras of smooth functions
The Picard group of noncommutative rings, in particular of orders
Yang-Mills-scalar-matter fields in the quantum Hopf fibration

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Geometric foundations for classical \(\mathrm{U}(1)\)-gauge theory on noncommutative manifolds