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

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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. 
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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