Irrational Uq(sl2)-symmetries on the quantum plane
Abstract
The main result of this work is to present the complete list of Uq(sl2)-symmetries of quantum plane. For that, the structure of quantum plane automorphisms is used. Our idea in classifying the above symmetries is in introducing some special symbolic matrices to label the series of actions in question. The matrices depict which generators of Uq(sl2) produce nonzero images by acting on the generators of quantum plane. This data determines the weights of an action unambiguously. It turns out that there are uncountably many isomorphism classes of the symmetries. Another result is in describing composition series of the corresponding representations. The classical limit of the above symmetries is given.
Cite
@article{arxiv.1003.0342,
title = {Irrational Uq(sl2)-symmetries on the quantum plane},
author = {Steven Duplij and Sergey Sinel'shchikov},
journal= {arXiv preprint arXiv:1003.0342},
year = {2010}
}
Comments
This paper was submitted to the arXiv as a concise preliminary version (without complete proofs and some additional material) of our preprint 0905.1719. Nevertheless, the removed preprint contained some material (e.g. classical limits and tables) which was absent in the full version 0905.1719. We decided to include this extra material to 0905.1719 and to withdraw the concise version