Geodesic
Lie rings defined by the root system and family of additive subgroups of the main ring
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 195-200 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a given carpet of additive subgroups, a carpet subring of the Chevalley algebra is defined. For this subring, an analog of the known question on the absence of new root elements in a carpet subgroup is answered and necessary and sufficient conditions of its invariance with respect to the corresponding carpet subgroup are found.
Keywords: Chevalley group and algebra, carpet of additive subgroups, Lie ring. 
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Ya. N. Nuzhin. Lie rings defined by the root system and family of additive subgroups of the main ring. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 195-200. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a22/

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