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29 March 2024
 
  » arxiv » math.QA/0407483

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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 ;
Date 28 Jul 2004
Journal Czech.J.Phys. 54 (2004) 1297-1303
Subject Quantum Algebra | math.QA hep-th
AbstractQuantum 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;iota)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part.
Source arXiv, math.QA/0407483
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