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

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

2004-07-28

arxiv.org/abs/math/0407483v1

Czech.J.Phys. 54 (2004) 1297-1303

Mathematics

Quantum Algebra

Talk given at the XIII Int. Coll. on Integrable Systems and Quantum Groups, June 17-19, 2004, Prague, Czech Republic. Submitte

Scientific paper

10.1007/s10582-004-9792-0

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;\iota)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part.

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