Michel Dubois--Violette, Peter W. Michor
The Frölicher-Nijenhuis bracket for derivation based non commutative differential forms
The paper is published: as ``More on the Frölicher-Nijenhuis bracket in non-commutative geometry, J. Pure and Appl. Algebra 121 (1997) 107-135

MSC:

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

Abstract: In commutative differential geometry the
Fr\"olicher-Nijenhuis bracket computes all kinds of curvatures and
obstructions to integrability. In \cit!{3} the Fr\"olicher-Nijenhuis
bracket was developped for universal differential forms of
non-commutative algebras, and several applications were given.
In this paper this bracket and the Fr\"olicher-Nijenhuis calculus will be
developped for several kinds of differential graded algebras based on
derivations, which were indroduced by \cit!{6}.

Keywords: Non-commutative geometry, derivations, Froelicher-Nijenhuis bracket, Kaehler differentials, graded differential algebra