Elementary parabolic twist

Details Elementary parabolic twist Elementary parabolic twist

2001-07-04

arxiv.org/abs/math/0107034v1

Mathematics

Quantum Algebra

9 pages, Latex 2e

Scientific paper

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 F_P 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 F_EJ and the new factor F_D. 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.

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