2000/10/31 by David Ananikian, Ananikian, David, Petr Kulish +5
Mathematics · #17B37 #20G42 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:20G42
paper · pdf · doi:10.48550/arxiv.math/0010312
10 pages, LaTeX-2e, to be published in the Proceedings of XXIII International Colloquium on Group-Theoretical Methods in Physics, Dubna, 31.07-05.08, 2000
arxiv created 2000/10/31 · openalex publication_date 2000/10/31 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Serious difficulties arise in the construction of chains of twists for symplectic Lie algebras. Applying the canonical chains of extended twists to deform the Hopf algebras U(sp(N)) one is forced to deal only with improper chains (induced by the U(sl(N)) subalgebras). In the present paper this problem is solved. For chains of regular injections the sets of maximal extended jordanian twists FE,k are considered. We prove that there exists for U(sp(N)) the twist FB,k composed of the factors FE,k. It is demonstrated that the twisting procedure deforms the space of the primitive subalgebra sp(N-1). The recursive algorithm for such deformation is found. This construction generalizes the results obtained for orthogonal classical Lie algebras and demonstrates the universality of primitivization effect for regular chains of subalgebras. For the chain of maximal length the twists FB,k,max become full, their carriers contain the Borel subalgebra B(sp(N)). Using such twisting procedures one can obtain the explicit quantizations for a wide class of classical r-matrices. As an example the full chain of extended twists for U(sp(3)) is considered.