Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups
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 -plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup and corresponding quantum superspace are considered in Cartesian basis. The contracted quantum superspace is interpreted as the non-commutative analog of the superspace with the fiber odd part.
Keywords
Cite
@article{arxiv.math/0407483,
title = {Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups},
author = {N. A. Gromov and D. B. Efimov and I. V. Kostyakov and V. V. Kuratov},
journal= {arXiv preprint arXiv:math/0407483},
year = {2009}
}
Comments
Talk given at the XIII Int. Coll. on Integrable Systems and Quantum Groups, June 17-19, 2004, Prague, Czech Republic. Submitted in Czech. J. of Physics