Dictionary on lie algebras and superalgebras

By L. Frappat, A. Sciarrino, P. Sorba. 2000

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Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras (2006, background): “The related theory helps us work towards completely classifying integrable equations from an algebraic point of view, because any Lie algebra has a semi-direct sum structure of a solvable Lie algebra and a semi-simple Lie algebra [5, 6].”
Semi-direct sums of Lie algebras and continuous integrable couplings (2006, background): “Recall that an arbitrary Lie algebra has a semi-direct sum structure of a solvable Lie algebra and a semi-simple Lie algebra [9].”
Semidirect sums of Lie algebras and discrete integrable couplings (2006, background): “Now, note that an arbitrary Lie algebra has a semi-direct sum structure of a solvable Lie algebra and a semi-simple Lie algebra [8], and we will see that semi-direct sums of Lie algebras can result in integrable couplings.”
Chevalley Supergroups (2008, methodology): “If g 6∈ { A(1, 1), P (3), Q(n) } , we take as Π a subset of ∆ in which αi ∈ ∆0 for all but one index i , and such that any α ∈ ∆ is either a sum of some αi’s — then it is called positive — or the opposite of such a sum — then it is called negative (when g is basic, fixing Π is equivalent to fix a sp”