L. D\c{a}browski L., Hajac P.M., Landi G., Siniscalco P.
Metrics and Pairs of Left and Right Connections on Bimodules
(49K, LaTeX, 16 pages)

ABSTRACT.  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 algebra of matrix 
valued functions, and an $SL\sb q(2,\IC)$-covariant calculus of the 
quantum plane plane at a generic $q$ and the cubic root of unity. 
It is shown that, in the aforementioned examples, giving up the 
middle-linearity of metrics significantly enlarges the space of metrics.
A~metric compatibility condition for the pairs of left and right
connections is defined. Also, a compatibility condition between a left and right
connection is discussed. Consequences entailed by reducing to the centre of a
bimodule the domain of those conditions are investigated in detail.
Alternative ways of relating left and right connections are considered. \\
Report-no: SISSA 26/96/FM; QDSM-Trieste/362