Non-commutative low-dimension spaces and superspaces associated with contracted quantum groups and supergroups. (English) Zbl 1465.58004
Summary: Quantum planes, which correspond to all one-parameter solutions of quantum Yang-Baxter equation (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 \(G L_q (1|2)\) 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.
MSC:
| 58B32 | Geometry of quantum groups |
| 46L87 | Noncommutative differential geometry |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
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