Geodesic
Factorization problem with intersection
Ufa mathematical journal, Tome 6 (2014) no. 1, pp. 3-11 Cet article a éte moissonné depuis la source Math-Net.Ru

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We propose a generalization of the factorization method to the case when $\mathcal G$ is a finite-dimensional Lie algebra $\mathcal G=\mathcal G_0\oplus M\oplus N$ (direct sum of vector spaces), where $\mathcal G_0$ is a subalgebra in $\mathcal G$, $M,N$ are $\mathcal G_0$-modules, and $\mathcal G_0+M$, $\mathcal G_0+N$ are subalgebras in $\mathcal G$. In particular, our construction involves the case when $\mathcal G$ is a $\mathbb Z$-graded Lie algebra. Using this generalization, we construct certain top-like systems related to algebra $so(3,1)$. According to the general scheme, these systems can be reduced to solving systems of linear equations with variable coefficients. For these systems we find polynomial first integrals and infinitesimal symmetries.
Keywords: factorization method, Lie algebra, integrable dynamical systems. 
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R. A. Atnagulova; O. V. Sokolova. Factorization problem with intersection. Ufa mathematical journal, Tome 6 (2014) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/UFA_2014_6_1_a0/

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