2001/09/13 by David Ananikian, Ananikian, David, Petr Kulish +5
Mathematics · Physics and Astronomy · #17B37 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:17B37 #msc:20G42
paper · pdf · doi:10.48550/arxiv.math/0109083
27 pages, LaTex 2e
arxiv created 2001/09/13 · openalex publication_date 2001/09/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of constructing the explicit form for full twist deformations of simple Lie algebras g with twist carriers containing the maximal nilpotent subalgebra N+(g) is studied. Our main tool is the sequence of regular subalgebras gi in U(g) that become primitive under the action of extended jordanian twists FE: U(g) -> UE(g). It is demonstrated that the structure of the sequence gi is defined by the extended Dynkin diagram of algebra g. To construct the injection of gi in UE(g) the special deformations of algebras UE(g) are performed. They are reduced to the (cohomologically trivial) twists Fs. Thus it is proved that full chains of twists can be written in the canonical form FB = F'N ... F'2F'1. The links F'i in such chains must contain not only the extended twists FE but also the factors Fs whose form depend on the type of the series of classical algebra g. The explicit forms of universal R-matrices (and the R-matrices in the fundamental representations) corresponding to full chains of twists for classical simple Lie algebras are found. The properties of the construction are illustrated by the example of full chain of extended twists for algebra sp(3).