English

Parabolic twists for algebras sl(n)

Quantum Algebra 2007-05-23 v2 Rings and Algebras

Abstract

New solutions of twist equations for universal enveloping algebras U(A_{n-1}) are found. They can be presented as products of full chains F_c of extended Jordanian twists, Abelian factors (rotations) F^R and sets of quasi-Jordanian twists F^J. The latter are the generalizations of Jordanian twists (with 2-dimensional Borel carrier b^2) for special deformed extensions of the Hopf algebra U(b^2). The carrier subalgebra g_P for the composition of these three twists is a nonminimal parabolic subalgebra in sl(n). The parabolic twisting elements F_P are obtained in the explicit form. The details of the construction are illustrated for the examples n=4 and n=11.

Keywords

Cite

@article{arxiv.math/0510295,
  title  = {Parabolic twists for algebras sl(n)},
  author = {V. D. Lyakhovsky},
  journal= {arXiv preprint arXiv:math/0510295},
  year   = {2007}
}

Comments

24 pages, LaTeX2e, Lemma 3 simplified, minor grammatical changes

R2 v1 2026-07-22T17:25:55.320Z