Lie bracket of vector fields in noncommutative geometry

Details Lie bracket of vector fields in noncommutative geometry Lie bracket of vector fields in noncommutative geometry

2003-06-02

arxiv.org/abs/math/0306044v1

Mathematics

Rings and Algebras

Latex, 19 pages

Scientific paper

10.1023/A:1025966331750

The aim of this paper is to avoid some difficulties, related with the Lie bracket, in the definition of vector fields in a non commutative setting, as they were defined by Woronowicz, Schmudgen--Schuler and Aschieri--Schupp. We extend the definition of vector fields to consider them as derivations of the algebra, through Cartan pairs introduced by Borowiec. Then, using translations, we introduce the invariant vector fields. Finally, the definition of Lie bracket realized by Dubois--Violette, considering elements in the center of the algebra, is also extended to these invariant vector fields.

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