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## Root systems in number fields

arxiv.org. math. Cornell University, 2018. No. 1808.01136.
Popov V. L., Zarhin Y. G.
We classify the types of root systems $R$ in the rings of integers of number fields  $K$ such that the Weyl group $W(R)$ lies in the group $\mathcal L(K)$ generated by ${\rm Aut} (K)$ and multipli\-ca\-tions by the elements of $K^*$. We also classify the Weyl groups of roots systems of rank $n$ which are isomorphic to a subgroup of $\mathcal L(K)$ for a number field $K$ of degree $n$ over $\mathbb Q$.