Jets and connections in commutative and noncommutative geometry
@inproceedings{LMangiarotti1999JetsAC, title={Jets and connections in commutative and noncommutative geometry}, author={L.Mangiarotti and G.Sardanashvily}, year={1999} }
It is emphasized that equivalent definitions of connections on modules over a commutative ring are not so in noncommutative geometry.
References
SHOWING 1-10 OF 12 REFERENCES
Noncommutative differential geometry of matrix algebras
- Mathematics
- 1990
The noncommutative differential geometry of the algebra Mn (C) of complex n×n matrices is investigated. The role of the algebra of differential forms is played by the graded differential algebra…
Le langage des espaces et des groupes quantiques
- Mathematics
- 1993
We study the foundations of the differential calculus in quantum geometry. The notions of (differential) quantum space and cone are introduced. Generalizing a construction of Manin, to a quantum cone…
Non-commutative Differential Geometry
- Mathematics, Biology
- 1998
This chapter is an exposition, without any proof or detail, of some topics in Non-Commutative Differential Geometry (NCDG), which involve the cyclic theory.
Linear connections on matrix geometries
- Mathematics
- 1995
A general definition of a linear connection in non-commutative geometry has recently been proposed. Two examples are given of linear connections in non-commutative geometries which are based on…
An Introduction to Noncommutative Spaces and Their Geometries
- Mathematics
- 1997
Noncommutative Spaces and Algebras of Functions.- Projective Systems of Noncommutative Lattices.- Modules as Bundles.- A Few Elements of K-Theory.- The Spectral Calculus.- Noncommutative Differential…
Linear connections on fuzzy manifolds
- Mathematics
- 1996
Linear connections are introduced on a series of non-commutative geometries which have commutative limits. Quasicommutative corrections are calculated.
Metrics and pairs of left and right connections on bimodules
- Mathematics
- 1996
Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1‐forms. Those bimodules are obtained from the derivation based calculus of an…