Metrics and Pairs of Left and Right Connections on Bimodules
Dcabrowski, L. ; Hajac, P. M. ; Landi, G. ; Siniscalco, P.
arXiv, 9602035 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1996-02-29
Classification:  Mathematics - Quantum Algebra,  General Relativity and Quantum Cosmology,  Mathematical Physics 
@article{9602035,
     author = {Dcabrowski, L. and Hajac, P. M. and Landi, G. and Siniscalco, P.},
     title = {Metrics and Pairs of Left and Right Connections on Bimodules},
     journal = {arXiv},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9602035}
}

Dcabrowski, L.; Hajac, P. M.; Landi, G.; Siniscalco, P. Metrics and Pairs of Left and Right Connections on Bimodules. arXiv, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/9602035/