Article
Ufa Mathematical Journal
Volume 6, Number 1, pp. 3-11
Factorization problem with intersection
Atnagulova R.A., Sokolova O.V.
DOI:10.13108/2014-6-1-3
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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 $\Z$-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.