On automorphisms of infinite classical root systems (Q2755697)

Denote by \(\Delta\) an infinite rank root system of type \(A_\infty\), \(A_{-\infty}\), \(B_\infty\), \(C_\infty, \) or \(D_\infty\). It is clear that for any \(l\in \{0\}\cup N\) there exists a finite root system \(\Delta_l\) such that \(\Delta_0\subset \Delta_1\subset\dots\) and \(\Delta=\bigcup_{l=0}^\infty \Delta_l\). For any nonnegative integer sequence \(n_1<n_2<\dots\), this paper gives an explicit construction of the automorphism subgroup of \(\Delta\) which preserves all \(\Delta_{n_i}\). It generalizes the usual construction of automorphism group of classical finite-dimensional Lie algebras.