On a class of skew classical r-matrices with large carrier
Abstract
Classical r-matrices with carriers g_c containing the Borel subalgebra b(+,g) of simple Lie algebra g are studied. Using the graphycal presentation of the dual Lie algebra g#(r) we show that such solutions of the CYBE always exist. To obtain the explicit form of these r-matrices we find the dual coordinates in which the adjoint action of g_c can be reduced. This gives us the detailed structure of the Jordanian r-matrices that are the candidates for enlarging the initial full chain r-matrix. We search the desired solution in the factorized form. This leads to the unique transformation: the initial chain is to be substituted by a special kind of peripheric r-matrice. To illustrate the method we consider the case of g=sl(11) in full details.
Cite
@article{arxiv.math/0410486,
title = {On a class of skew classical r-matrices with large carrier},
author = {Vladimir D. Lyakhovsky},
journal= {arXiv preprint arXiv:math/0410486},
year = {2007}
}
Comments
15 pages