dorsal/arxiv
View SchemaMetrics and Pairs of Left and Right Connections on Bimodules
| Authors | L. Dcabrowski, P. M. Hajac, G. Landi, P. Siniscalco |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9602035 |
| URL | https://arxiv.org/abs/q-alg/9602035 |
| DOI | 10.1063/1.531644 |
| Journal | J.Math.Phys. 37 (1996) 4635-4646 |
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.
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"abstract": "Properties of metrics and pairs consisting of left and right connections are\nstudied on the bimodules of differential 1-forms. Those bimodules are obtained\nfrom the derivation based calculus of an algebra of matrix valued functions,\nand an $SL\\sb q(2,\\IC)$-covariant calculus of the quantum plane plane at a\ngeneric $q$ and the cubic root of unity. It is shown that, in the\naforementioned examples, giving up the middle-linearity of metrics\nsignificantly enlarges the space of metrics. A~metric compatibility condition\nfor the pairs of left and right connections is defined. Also, a compatibility\ncondition between a left and right connection is discussed. Consequences\nentailed by reducing to the centre of a bimodule the domain of those conditions\nare investigated in detail. Alternative ways of relating left and right\nconnections are considered.",
"arxiv_id": "q-alg/9602035",
"authors": [
"L. Dcabrowski",
"P. M. Hajac",
"G. Landi",
"P. Siniscalco"
],
"categories": [
"q-alg",
"gr-qc",
"math-ph",
"math.MP",
"math.QA"
],
"doi": "10.1063/1.531644",
"journal_ref": "J.Math.Phys. 37 (1996) 4635-4646",
"title": "Metrics and Pairs of Left and Right Connections on Bimodules",
"url": "https://arxiv.org/abs/q-alg/9602035"
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