arXiv subjects
Publications and source records attributed to Alexei Vladimirov.
We outline the proofs of several principal statements in conventional renormalization theory. This may be of some use in the light of new trends and new techniques (Hopf algebras, etc.) recently introduced in the field.
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.