2008/09/01 by Enrico Celeghini, E. Celeghini, Celeghini, Enrico
Mathematics · Physics and Astronomy · #17B35 #17B37 #17B62 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B35 #msc:17B37 #msc:17B62 #msc:81R50
paper · pdf · doi:10.48550/arxiv.0809.0264
Latex, 10 pages, no figures
arxiv created 2008/09/01 · openalex publication_date 2008/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to analize inside the infinitely many possible bases of Uq(g), same that can be considered "more equal then others". The element of selection has been a privileged relation with the bialgebra. A new parameter z' has been found that determines the commutation relations, independent from the z=log(q) that defines Uq(g). Both z and z' are necessary to fix the relations between the basic set and its coproducts. Three cases are particularly relevant: the analytical set with z'=z, the Lie set with Lie-like commutation relations (for z'=0) and the canonical/crystal basis with z' infinity. To simplify the exposition, we discuss in details the easy generalizable case of Uq(su(2)).