Abstract:
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.
Citation:
Ya. N. Nuzhin, “Lie rings defined by the root system and family of additive subgroups of the main ring”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 195–200; Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 119–125
\Bibitem{Nuz12}
\by Ya.~N.~Nuzhin
\paper Lie rings defined by the root system and family of additive subgroups of the main ring
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 3
\pages 195--200
\mathnet{http://mi.mathnet.ru/timm853}
\elib{https://elibrary.ru/item.asp?id=17937025}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 283
\issue , suppl. 1
\pages 119--125
\crossref{https://doi.org/10.1134/S0081543813090125}
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Linking options:
https://www.mathnet.ru/eng/timm853
https://www.mathnet.ru/eng/timm/v18/i3/p195
This publication is cited in the following 6 articles:
Yakov N. Nuzhin, “On the closedness of carpets of additive subgroups associated with a Chevalley group over a commutative ring”, Zhurn. SFU. Ser. Matem. i fiz., 16:6 (2023), 732–737
P. S. Badin, Ya. N. Nuzhin, E. N. Troyanskaya, “O slabo dopolnyaemykh kovrakh lieva tipa nad kommutativnymi koltsami”, Vladikavk. matem. zhurn., 23:4 (2021), 28–34
Gutnova A.K. Koibaev V.A., “on Sufficient Conditions For the Closure of An Elementary Net”, Vestn. St Petersb. Univ.-Math., 53:2 (2020), 145–148
Bashkirov E.L., “On a Class of Lie Rings of 2 X 2 Matrices Over Associative Commutative Rings”, Linear Multilinear Algebra, 67:3 (2019), 456–478
V. A. Koibaev, Ya. N. Nuzhin, “Subgroups of the Chevalley groups and Lie rings definable by a collection of additive subgroups of the initial ring”, J. Math. Sci., 201:4 (2014), 458–464
Koibaev V.A., Nuzhin Ya.N., “Podgruppy grupp shevalle i koltsa li, opredelyaemye naborom additivnykh podgrupp osnovnogo koltsa”, Matematicheskii forum (itogi nauki. yug Rossii), 6 (2012), 44–55
Subgroups of the Сhevalley groups and lie rings determined by a set of additive subgroups of the initial ring
Citation in format AMSBIB
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