2003/12/09 by V. D. Lyakhovsky, Vladimir Lyakhovsky, Lyakhovsky, Vladimir
Engineering · Mathematics · #17B37 #20G42 #81R50 #FOS: Mathematics #Geophysics and Sensor Technology #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:20G42 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/0312185
17 pages
arxiv created 2003/12/09 · openalex publication_date 2003/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Twist deformation UF(g) is equivalent to the quantum group Fund(G#) and has two preferred bases: the one originating from U(g) and that of the coordinate functions on the dual Lie group G#. The costructure of the Hopf algebra UF(g) is analized in terms of group G#. The weight diagram of the adjoint representation of the algebra g# is constructed in terms of the root system L(g). The explicit form of the g --> g# transformation can be obtained for any simple Lie algebra g and the factorizable chain F of extended Jordanian twists. The dual group approach is used to find new solutions of the twist equations. The parametrized family of extended Jordanian deformations for U(sl(3)) is constructed and studied in terms of SL(3)#. New realizations of the parabolic twist are found.