The faithful enveloping rings of the nil-triangular ring of type $G_2$ and their automorphisms

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.