Article
Ufa Mathematical Journal
Volume 4, Number 3, pp. 6-16
New solutions of Yang-Baxter Equation with the square.
Atnagulova R.A., Golubchik I.Z.
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In the theory of integrable differential equations play an important role of the Yang-Baxter equation with the square, that is, the equation $R([R(a),b]-[R(b),a])=R^{2}([a,b])+[R(a),R(b)]$, where $a,b\in g$, $g$ --- Lie algebra, and $R$ --- linear operator space $g$. To construct examples of operators $R$ in use of the Lie subalgebra $h$ in the matrix algebra, additional to subspace of matrices with zero last row. Are two series of examples of such subalgebras $h$.