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 ₁₂ T ₁ T ₂ = T ₂ T ₁ R ₁₂, E ₁ T ₂ = T ₂ E ₁ R ₁₂, 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 U _q(g) can be naturally imposed on Yang-Baxter algebras from the requirement of non-degeneracy of the pairing.