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
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 GLq(1|2) and corresponding quantum superspace Cq(1|2) are considered in Cartesian basis. The contracted quantum superspace Ch(1|2;ι) is interpreted as the non-commutative analog of the superspace with the fiber odd part.
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