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Noncommutative Geometry of the h-deformed Quantum Plane

S. Cho·J. Madore·K. S. Park
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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 Poincaré half-plane, a surface of constant negative Gaussian curvature.

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S. Cho, J. Madore, K. S. Park. 1997-09-25. Noncommutative Geometry of the h-deformed Quantum Plane. https://doi.org/10.1088/0305-4470%2F31%2F11%2F013

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