2001/07/04 by V. D. Lyakhovsky, Vladimir Lyakhovsky, Lyakhovsky, Vladimir +2
Mathematics · #17B37 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:20G42
paper · pdf · doi:10.48550/arxiv.math/0107034
9 pages, Latex 2e
arxiv created 2001/07/04 · openalex publication_date 2001/07/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The twist deformations for simple Lie algebras U(g) whose twisting elements F are known explicitly are usually defined on the carrier subspace injected in the Borel subalgebra B+(g). We solve the problem of creating the parabolic twist FP whose carrier algebra P not only covers B+(g) but also intersects nontrivially with B-(g). This algebra P is the parabplic subalgebra in sl(3) and has the structure of the algebra of two-dimensional motions. The parabolic twist is explicitly constructed as a composition of the well known extended jordanian twist FEJ and the new factor FD. The latter can be considered as a special version of the jordanian twist. The twisted costructure is found for U(P) and the corresponding universal R-matrix is presented.