Metrics on the Real Quantum Plane

G. Fiore; M. Maceda; J. Madore

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arXiv · math/0011177

Metrics on the Real Quantum Plane

G. Fiore·M. Maceda·J. Madore

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Abstract

Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition a metric maps the tensor product of two 1-forms into a `function' on the quantum plane. It is symmetric in a modified sense, namely in the definition of symmetry one has to replace the permutator map with a deformed map σfulfilling some suitable conditions. Correspondingly, also the definition of the hermitean conjugate of the tensor product of two 1-forms is modified (but reduces to the standard one if σcoincides with the permutator). The metric is real with respect to such modified *-structure.

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G. Fiore, M. Maceda, J. Madore. 2002-09-29. Metrics on the Real Quantum Plane. https://arxiv.org/abs/math/0011177

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