2005/10/14 by V. D. Lyakhovsky, Lyakhovsky, V. D.
Mathematics · Physics and Astronomy · #17B37 #20G42 #81R50 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:17B37 #msc:20G42 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/0510295
24 pages, LaTeX2e, Lemma 3 simplified, minor grammatical changes
openalex publication_date 2005/10/14 · arxiv created 2005/10/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
New solutions of twist equations for universal enveloping algebras U(An-1) are found. They can be presented as products of full chains Fc of extended Jordanian twists, Abelian factors (rotations) FR and sets of quasi-Jordanian twists FJ. The latter are the generalizations of Jordanian twists (with 2-dimensional Borel carrier b2) for special deformed extensions of the Hopf algebra U(b2). The carrier subalgebra gP for the composition of these three twists is a nonminimal parabolic subalgebra in sl(n). The parabolic twisting elements FP are obtained in the explicit form. The details of the construction are illustrated for the examples n=4 and n=11.