On derivations of some infinite-dimensional topologically nilpotent Lie algebras (Q923714)

The algebras considered in this paper are the Lie algebra \(M\) of infinite complex matrices containing only a finite number of nonzero entries and its nil subalgebras whose normalizers contain an upper triangular subalgebra. The author computes the algebra of derivations of three different classes of such subalgebras \(L\). The case division is based on properties of a certain subset of the set of positive roots which determines \(L\). The algebras of derivations encountered are sums of one, two, or three of the following subalgebras: all \(\text{ad}\, x\) for \(x\) in a certain algebra containing \(L\), all endomorphisms of \(L\) with image in the center of \(L\) and vanishing on \([L,L]\), and the linear envelope of certain derivations easily defined in terms of their action on root spaces.