Classical Yang-Baxter Equation and Low Dimensional Triangular Lie Bialgebras
Abstract
All solutions of constant classical Yang-Baxter equation (CYBE) in Lie algebra
L
with dim
L≤3
are obtained and the sufficient and necessary conditions which
(L,[ ],
Δ
r
,r)
is a coboundary (or triangular) Lie bialgebra are given. The strongly symmetric elements in
L⊗L
are found and they all are solutions of CYBE in
L
with
dimL≤3
.