1998/08/17 by Mirko Luedde, Luedde, Mirko, Alexei Vladimirov +1
Mathematics · #16W30 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W30
paper · pdf · doi:10.48550/arxiv.math/9808075
6 pages, LaTeX, no figures, presented at the 7th Colloquium ``Quantum Groups and Integrable Systems", Prague, June 1998
arxiv created 1998/08/17 · arxiv updated 2009/11/30
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, Δ(T) = T ⊗ T, Δ(E) = E ⊗ T + 1 ⊗ 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 Uq(g) can be naturally imposed on Yang-Baxter algebras from the requirement of non-degeneracy of the pairing.