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On globally non-trivial almost-commutative manifolds

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posted on 2024-11-15, 11:23 authored by Jord Boeijink, Koenraad van den Dungen
Within the framework of Connes’ noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a “principal module,” which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of “gauge modules,” and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.

History

Citation

Boeijink, J. and van den Dungen, K. (2014). On globally non-trivial almost-commutative manifolds. Journal of Mathematical Physics, 55 (10), 103508-1 - 103508-33.

Journal title

Journal of Mathematical Physics

Volume

55

Issue

10

Pagination

103508

Language

English

RIS ID

96032

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