Full chains of twists for symplectic algebras

Details Full chains of twists for symplectic algebras Full chains of twists for symplectic algebras

2001-09-13

arxiv.org/abs/math/0109083v1

Mathematics

Quantum Algebra

27 pages, LaTex 2e

Scientific paper

The problem of constructing the explicit form for full twist deformations of simple Lie algebras g with twist carriers containing the maximal nilpotent subalgebra N^+(g) is studied. Our main tool is the sequence of regular subalgebras g_i in U(g) that become primitive under the action of extended jordanian twists F_E: U(g) -> U_E(g). It is demonstrated that the structure of the sequence {g_i} is defined by the extended Dynkin diagram of algebra g. To construct the injection of g_i in U_E(g) the special deformations of algebras U_E(g) are performed. They are reduced to the (cohomologically trivial) twists F_s. Thus it is proved that full chains of twists can be written in the canonical form F_B = F'_N ... F'_2F'_1. The links F'_i in such chains must contain not only the extended twists F_E but also the factors F_s whose form depend on the type of the series of classical algebra g. The explicit forms of universal R-matrices (and the R-matrices in the fundamental representations) corresponding to full chains of twists for classical simple Lie algebras are found. The properties of the construction are illustrated by the example of full chain of extended twists for algebra sp(3).

Affiliated with

Also associated with

No associations

Rating

Full chains of twists for symplectic algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Full chains of twists for symplectic algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Full chains of twists for symplectic algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-540800