Analogs of q-Serre relations in the Yang-Baxter algebras
Quantum Algebra
2007-05-23 v1
Abstract
Yang-Baxter bialgebras, as previously introduced by the authors, are shown to arise from a double crossproduct construction applied to the bialgebra R T T = T T R, E T = T E R, \Delta(T) = T \hat{\otimes} T, \Delta(E) = E \hat{\otimes} T + 1 \hat{\otimes} E and its skew dual, with R being a numerical matrix solution of the Yang-Baxter equation. It is further shown that a set of relations generalizing q-Serre ones in the Drinfeld-Jimbo algebras U_q(g) can be naturally imposed on Yang-Baxter algebras from the requirement of non-degeneracy of the pairing.
Keywords
Cite
@article{arxiv.math/9808075,
title = {Analogs of q-Serre relations in the Yang-Baxter algebras},
author = {Mirko Luedde and Alexei Vladimirov},
journal= {arXiv preprint arXiv:math/9808075},
year = {2007}
}
Comments
6 pages, LaTeX, no figures, presented at the 7th Colloquium ``Quantum Groups and Integrable Systems", Prague, June 1998