All possible Cayley-Klein contractions of quantum orthogonal groups |
| |
Authors: | N A Gromov V V Kuratov |
| |
Institution: | (1) Department of Mathematics, Komi Science Center, Ural Division, Russian Academy of Sciences, Syktyvkar, 167982, Russia |
| |
Abstract: | Spaces of constant curvature and their motion groups are described most naturally in the Cartesian basis. All these motion groups, also known as CK groups, are obtained from an orthogonal group by contractions and analytical continuations. On the other hand, quantum deformation of orthogonal group SO(N) is most easily performed in the so-called symplectic basis. We reformulate its standard quantum deformation to the Cartesian basis and obtain all possible contractions of quantum orthogonal group SO q (N) for both untouched and transformed deformation parameters. It turned out that, similar to the undeformed case, all CK contractions of SO q (N) are realized. An algorithm for obtaining nonequivalent (as Hopf algebra) contracted quantum groups is suggested. Contractions of SO q (N), N = 3, 4, 5, are regarded as examples. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|