A presentation for the Virasoro and super-Virasoro algebras (Q1106929)

The authors provide a set of generators and relations for the Virasoro, and super-Virasoro algebras. It is clear that the Virasoro algebra is generated by the elements \((L_ 1,L_ 2,L_{-1},L_{-2})\); it follows easily that, in fact, any pair \((L_ n,L_{n+1})\), for \(n\geq 3\) generates it. The authors prove that starting with the pair \((L_ 3,L_{-2})\), and imposing eight relations, determines the algebra completely. Similar results are proved for the super Virasoro algebras.