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Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups

N. A. Gromov·D. B. Efimov·I. V. Kostyakov·V. V. Kuratov
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Abstract

Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum $h$-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup $ GL_q(1|2)$ and corresponding quantum superspace $ C_q(1|2)$ are considered in Cartesian basis. The contracted quantum superspace $ C_h(1|2;ι)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part.

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N. A. Gromov, D. B. Efimov, I. V. Kostyakov, V. V. Kuratov. 2004-07-28. Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups. https://doi.org/10.1007/s10582-004-9792-0

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