Lattices of root type in Lie algebras \(D_{2^ m}\) and \(B_{2^ m- 1}\) (Q583344)

In his previous paper [Usp. Mat. Nauk 44, No.1(265), 217-218 (1989; Zbl 0679.17003)], the author has communicated that the lattices of root type are considered in another paper. Now here the automorphism groups of invariant sublattices of root type arising in a multiplicative orthogonal decomposition of simple Lie algebras \({\mathcal L}\) of type \(D_{2^ m}\) and \(B_{2^ m-1}\) (m\(\geq 2)\) are described. Remark. The titles of the original paper and its English translation contain the same mistake: \(B_{2^{m-1}}\) instead of \(B_{2^ m-1}\).