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Among the simple finite dimensional Lie algebras, only sl(n) possesses twoautomorphisms of finite order which have no common nonzero eigenvector witheigenvalue one. It turns out that these automorphisms are inner and form a pairof generators that allow one to generate all of sl(n) under bracketing. Itseems that Sylvester was the first to mention these generators, but he usedthem as generators of the associative algebra of all n times n matrices Mat(n).These generators appear in the description of elliptic solutions of theclassical Yang-Baxter equation, orthogonal decompositions of Lie algebras, 'tHooft's work on confinement operators in QCD, and various other instances. HereI give an algorithm which both generates sl(n) and explicitly describes a setof defining relations. For simple (up to center) Lie superalgebras, analogs ofSylvester generators exist only for sl(n|n). The relations for this case arealso computed.Comment: 14 pages, 6 figure

Sylvester-’t Hooft generators and relations between them for $$\mathfrak{s}\mathfrak{l}(n)$$ and $$\mathfrak{g}\mathfrak{l}(n|n)$$