dorsal/arxiv
View SchemaDifferential Calculi and Linear Connections
| Authors | Aristophanes Dimakis, J. Madore |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9601023 |
| URL | https://arxiv.org/abs/q-alg/9601023 |
| DOI | 10.1063/1.531645 |
Abstract
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.
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"abstract": "A method is proposed for defining an arbitrary number of differential calculi\nover a given noncommutative associative algebra. As an example the generalized\nquantum plane is studied. It is found that there is a strong correlation, but\nnot a one-to-one correspondence, between the module structure of the 1-forms\nand the metric torsion-free connections on it. In the commutative limit the\nconnection remains as a shadow of the algebraic structure of the 1-forms.",
"arxiv_id": "q-alg/9601023",
"authors": [
"Aristophanes Dimakis",
"J. Madore"
],
"categories": [
"q-alg",
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],
"doi": "10.1063/1.531645",
"title": "Differential Calculi and Linear Connections",
"url": "https://arxiv.org/abs/q-alg/9601023"
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