The faithful enveloping rings of the nil-triangular ring of type $G_2$ and their automorphisms
Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 118-142
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The structure of the Chevalley algebra over a field or ring $K$, associated with an indecomposable root system $\Phi$, essentially depends on its nil-triangular subalgebra $N\Phi(K)$. It turned out to be natural for $N\Phi(K)$ to use the faithful enveloping algebra $R$, introduced in 2018, which has the same basis as $N\Phi(K)$. It is known that the isomorphism of the Lie rings $N\Phi(K)$ does not depend on the choice of signs of the structure constants $N_{r, s}$. However, for faithful enveloping rings $R$ this property is violated. Therefore, the question of describing their automorphisms was extended to finding all non-isomorphic faithful enveloping rings $N\Phi(K)$ of type $G_2$ over $K$, and only then finding an explicit description of their automorphisms.
Keywords:
Lie algebra, Chevalley algebra, faithful enveloping algebra, standard automorphism, upper central series, hypercentral automorphism.
Mots-clés : nil-triangular subalgebra
Mots-clés : nil-triangular subalgebra
@article{CHEB_2024_25_3_a7,
author = {A. V. Kazakova},
title = {The faithful enveloping rings of the nil-triangular ring of type $G_2$ and their automorphisms},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {118--142},
year = {2024},
volume = {25},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_3_a7/}
}
A. V. Kazakova. The faithful enveloping rings of the nil-triangular ring of type $G_2$ and their automorphisms. Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 118-142. http://geodesic.mathdoc.fr/item/CHEB_2024_25_3_a7/