1998/06/03 by P. P. Kulish, V. D. Lyakhovsky, Andrey Mudrov +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA
paper · pdf · doi:10.1063/1.532987
28 pages, LaTeX
arxiv created 1998/06/03 · openalex publication_date 1999/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B∨ of sl(N) the explicit expressions are obtained for the twist element ℱ, universal ℛ-matrix and the corresponding canonical element 𝒯. It is shown that the twisted Hopf algebra UF(B∨) is self-dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld–Jimbo quantization to the Jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.