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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 | 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;iota)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part. | Source: | arXiv, math.QA/0407483 | Services: | Forum | Review | PDF | Favorites |
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