dorsal/arxiv
View SchemaNoncommutative Geometry of the h-deformed Quantum Plane
| Authors | S. Cho, J. Madore, K. S. Park |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709007 |
| URL | https://arxiv.org/abs/q-alg/9709007 |
| DOI | 10.1088/0305-4470/31/11/013 |
Abstract
The $h$-deformed quantum plane is a counterpart of the $q$-deformed one in the set of quantum planes which are covariant under those quantum deformations of GL(2) which admit a central determinant. We have investigated the noncommutative geometry of the $h$-deformed quantum plane. There is a 2-parameter family of torsion-free linear connections, a 1-parameter sub-family of which are compatible with a skew-symmetric non-degenerate bilinear map. The skew-symmetric map resembles a symplectic 2-form and induces a metric. It is also shown that the extended $h$-deformed quantum plane is a noncommutative version of the Poincar\'e half-plane, a surface of constant negative Gaussian curvature.
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"abstract": "The $h$-deformed quantum plane is a counterpart of the $q$-deformed one in\nthe set of quantum planes which are covariant under those quantum deformations\nof GL(2) which admit a central determinant. We have investigated the\nnoncommutative geometry of the $h$-deformed quantum plane. There is a\n2-parameter family of torsion-free linear connections, a 1-parameter sub-family\nof which are compatible with a skew-symmetric non-degenerate bilinear map. The\nskew-symmetric map resembles a symplectic 2-form and induces a metric. It is\nalso shown that the extended $h$-deformed quantum plane is a noncommutative\nversion of the Poincar\\\u0027e half-plane, a surface of constant negative Gaussian\ncurvature.",
"arxiv_id": "q-alg/9709007",
"authors": [
"S. Cho",
"J. Madore",
"K. S. Park"
],
"categories": [
"q-alg",
"gr-qc",
"math.QA"
],
"doi": "10.1088/0305-4470/31/11/013",
"title": "Noncommutative Geometry of the h-deformed Quantum Plane",
"url": "https://arxiv.org/abs/q-alg/9709007"
},
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