SU(n)-Connections and Noncommutative Differential Geometry

Details SU(n)-Connections and Noncommutative Differential Geometry SU(n)-Connections and Noncommutative Differential Geometry

1996-12-27

arxiv.org/abs/dg-ga/9612017v1

Mathematics

Differential Geometry

20 pages, LaTeX2e (use packages amstex, amssymb, theorem, a4, pb-diagram, lamsarrow)

Scientific paper

We study the noncommutative differential geometry of the algebra of endomorphisms of any SU(n)-vector bundle. We show that ordinary connections on such SU(n)-vector bundle can be interpreted in a natural way as a noncommutative 1-form on this algebra for the differential calculus based on derivations. We interpret the Lie algebra of derivations of the algebra of endomorphisms as a Lie algebroid. Then we look at noncommutative connections as generalizations of these usual connections.

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