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A functional model for the Lie algebra $\operatorname{ISO}(1,1)$ of linear non-self-adjoint operators
Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 79-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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A functional model is constructed for the Lie algebra $\operatorname{ISO}(1,1)$ of linear non-self-adjoint operators subject to the commutation relations $[A_1,A_2]=0$, $[A_1,A_3]=iA_2$, $[A_2,A_3]=iA_1$. The construction is based on a non-Abelian generalization of the Lax–Phillips scattering scheme on the group of transformations of the pseudo-Euclidean plane preserving the quadratic form $x^2-y^2$. 
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V. A. Zolotarev. A functional model for the Lie algebra $\operatorname{ISO}(1,1)$ of linear non-self-adjoint operators. Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 79-106. http://geodesic.mathdoc.fr/item/SM_1995_186_1_a4/

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