The faithful enveloping rings of the nil-triangular ring of type 𝐺2 and their automorphisms
https://doi.org/10.22405/2226-8383-2024-25-3-118-142
Abstract
The structure of the Chevalley algebra over a field or ring 𝐾, associated with an indecomposable root system Φ, essentially depends on its nil-triangular subalgebra 𝑁Φ(𝐾). It turned out to be natural for 𝑁Φ(𝐾) to use the faithful enveloping algebra 𝑅, introduced in 2018, which has the same basis as 𝑁Φ(𝐾). It is known that the isomorphism of the Lie rings 𝑁Φ(𝐾) does not depend on the choice of signs of the structure constants 𝑁𝑟,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 𝑁Φ(𝐾) of
type 𝐺2 over 𝐾, and only then finding an explicit description of their automorphisms.
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Review
For citations:
Kazakova A.V. The faithful enveloping rings of the nil-triangular ring of type 𝐺2 and their automorphisms. Chebyshevskii Sbornik. 2024;25(3):118-142. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-3-118-142
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