Invariant noncommutative connections

Details Invariant noncommutative connections Invariant noncommutative connections

2004-07-12

arxiv.org/abs/math-ph/0407022v1

Physics

Mathematical Physics

33 pages, latex

Scientific paper

10.1063/1.2131206

In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the ordinary geometry of connections. We use explicitely some geometric constructions usually introduced to classify ordinary invariant connections, and we expand them using algebraic objects coming from the noncommutative setting. The main result is that the classification can be performed using a ``reduced'' algebra, an associated differential calculus and a module over this algebra.

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