An element x of a Lie algebra L over the field F is extremal if [x,[x, L]]= F x. Under minor
assumptions, it is known that, for a simple Lie algebra L, the extremal geometry E (L) is a …

The origin of Lie theory is geometric and initialized with the view that the geometry of a
space is determined by the group of its symmetries. Motivated by the study of differential …

An extremal element $ x $ in a Lie algebra $\mathfrak {g} $ is an element for which the
space $[x,[x,\mathfrak {g}]] $ is contained in the linear span of $ x $. Long root elements in …

An extremal element in a Lie algebra g is a non-zero element x∈ g such that [x,[x, g]]⊆ Fx,
and we denote by E (g) the set of extremal elements of g. If, however,[x,[x, g]] is 0 …