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Quantum Bianchi identities via DG categories.
- Source :
-
Journal of Geometry & Physics . Jan2018, Vol. 124, p350-370. 21p. - Publication Year :
- 2018
-
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 S 3 and the bicrossproduct quantum spacetime [ r , t ] = λ r . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03930440
- Volume :
- 124
- Database :
- Academic Search Index
- Journal :
- Journal of Geometry & Physics
- Publication Type :
- Academic Journal
- Accession number :
- 127982385
- Full Text :
- https://doi.org/10.1016/j.geomphys.2017.11.005