Analogs of q-Serre relations in the Yang-Baxter algebras

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, Δ(T) = T \hat{\otimes} T, Δ(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.