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- W2771000212 abstract "We use DG categories to derive analogues of the Bianchi identities for the curvature of a connection in noncommutative differential geometry. We also revisit the Chern–Connes pairing but following the line of Chern’s original derivation. We show that a related DG category of extendable bimodule connections is a monoidal tensor category and in the metric compatible case obtain an analogue of a classical antisymmetry of the Riemann tensor. The monoidal structure implies the existence of a cup product on noncommutative sheaf cohomology. Another application shows that the curvature of a line module reduces to a 2-form on the base algebra. We illustrate the theory on the q-sphere, the permutation group S3 and the bicrossproduct quantum spacetime [r,t]=λr." @default.
- W2771000212 created "2017-12-04" @default.
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- W2771000212 date "2018-01-01" @default.
- W2771000212 modified "2023-09-30" @default.
- W2771000212 title "Quantum Bianchi identities via DG categories" @default.
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- W2771000212 doi "https://doi.org/10.1016/j.geomphys.2017.11.005" @default.
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