caa a22 4500 467911037 CHVBK 20180406152849.0 cr unu---uuuuu 170328e20061001xx s 000 0 eng 10.1007/s11232-006-0119-0 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0119-0 Sachse C. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany aut Sylvester-'t Hooft generators and relations between them for $$\mathfrak{s}\mathfrak{l}(n)$$ and $$\mathfrak{g}\mathfrak{l}(nn)$$ [Elektronische Daten] [C. Sachse] Among the simple finite-dimensional Lie algebras, only $$\mathfrak{s}\mathfrak{l}(n)$$ has two finite-order automorphisms that have no common nonzero eigenvector with the eigenvalue one. It turns out that these automorphisms are inner and form a pair of generators that allow generating all of $$\mathfrak{s}\mathfrak{l}(n)$$ under bracketing. It seems that Sylvester was the first to mention these generators, but he used them as generators of the associative algebra of all n×n matrices Mat(n). These generators appear in the description of elliptic solutions of the classical Yang-Baxter equation, the orthogonal decompositions of Lie algebras, 't Hooft's work on confinement operators in QCD, and various other instances. Here, we give an algorithm that both generates $$\mathfrak{s}\mathfrak{l}(n)$$ and explicitly describes a set of defining relations. For simple (up to the center) Lie superalgebras, analogues of Sylvester generators exist only for $$\mathfrak{g}\mathfrak{l}(n|n)$$ . We also compute the relations for this case. Springer Science+Business Media, Inc., 2006 defining relations nationallicence Lie algebras nationallicence Lie superalgebras nationallicence Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 149/1(2006-10-01), 1299-1311 0040-5779 149:1<1299 2006 149 11232 https://doi.org/10.1007/s11232-006-0119-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0119-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sachse C. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 149/1(2006-10-01), 1299-1311 0040-5779 149:1<1299 2006 149 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer