A family of \(\widetilde A_n\)-groups
The authors establish for each finite field \(k\), for each natural number \(n\geq 2\), and for each automorphism \(\sigma\) of \(k\), an automorphism group of the affine building \(\Delta\) of type \(\widetilde A_n\) associated to \(k(t)\) acting sharply transitively and type-rotating on the set of vertices of \(\Delta\). This uses the lattice construction of the affine building \(\Delta\) and generalizes earlier results for \(n=2,3\).
scientific article; zbMATH DE number 1250643