Mathematics – Differential Geometry
Scientific paper
1996-01-23
Mathematics
Differential Geometry
16 pages of LaTeX
Scientific paper
10.1063/1.531645
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a one-to-one correspondence, between the module structure of the 1-forms and the metric torsion-free connections on it. In the commutative limit the connection remains as a shadow of the algebraic structure of the 1-forms.
Dimakis Aristophanes
Madore John
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