2004/11/17 by A. Ballesteros, A Ballesteros, E. Celeghini +3
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Hopf algebra #Lie algebra #Quantization (signal processing) #Quantum #Quantum Information and Cryptography #Quantum algebra #math.GR #math.QA #msc:17B37 #msc:81R40 #msc:81R50
paper · pdf · doi:10.1088/0305-4470/38/18/003
published as J. Phys. A 38 (2005) · 23 pages, no figures
arxiv created 2004/11/17 · openalex publication_date 2005/04/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Hopf algebra quantizations of 4-dimensional and 6-dimensional real classical Drinfel'd doubles are studied by following a direct "analytic" approach. The full quantization is explicitly obtained for most of the Drinfel'd doubles, except a small number of them for which the dual Lie algebra is either sl(2) or so(3). In the latter cases, the classical r-matrices underlying the Drinfel'd double quantizations contain known standard ones plus additional twists. Several new four and six-dimensional quantum algebras are presented and some general features of the method are emphasized.