96-58 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) Mar 6, 96

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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

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