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- W2007407103 abstract "In this paper, we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct for every derivation X a module parallel transport, which is a lift to the module of the one-parameter group of algebra automorphisms generated by X. This parallel transport morphism is determined uniquely by an ordinary differential equation depending on the covariant derivative along X. Based on these parallel transport morphisms, we define a basic set of gauge invariant observables, i.e. functions from the space of connections to the complex numbers. For modules equipped with a Hermitian structure, we prove that this set of observables is separating on the space of gauge equivalence classes of Hermitian connections. This solves the gauge copy problem for fuzzy gauge theories." @default.
- W2007407103 created "2016-06-24" @default.
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- W2007407103 date "2014-03-01" @default.
- W2007407103 modified "2023-09-23" @default.
- W2007407103 title "Module parallel transports in fuzzy gauge theory" @default.
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- W2007407103 doi "https://doi.org/10.1142/s0219887814500212" @default.
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