On the dimensions of automorphism groups of eight-dimensional ternary fields. II
The automorphism group of a ternary field is naturally isomorphic to the stabilizer of a quadrangle in the collineation group of the corresponding projective plane. Consideration of compact projective planes of topological dimension 16 (these planes are relatives of the octonion plane) leads to locally compact ternary fields of topological dimension 8. Let \(\Gamma\) be the automorphism group of such a ternary field. The author proves that \(\Gamma\) is isomorphic to one of the compact groups \(G_2\) or \(\text{SU}_3 \mathbb{C}\), or \(\Gamma\) has topological dimension at most 7; actually, he obtains much more detailed information about \(\Gamma\). The proof is rather involved, by necessity, because at present it is not known if \(\Gamma\) is always compact, or a Lie group. [Part I has appeared in J. Geom. 52, No. 1-2, 30-40 (1995; see the review above)].
scientific article; zbMATH DE number 727305
scientific article