Projective uniformization and graded Lie algebras over Riemann surfaces (Q1191340)

It is shown that two of the main conceptual notions of supersymmetry and superstring theory -- those of a graded Lie algebra (= Lie superalgebra) and super Riemann surface -- are natural satellites of the concept of an ordinary Riemann surface. Namely, to any Riemann surface \(S\) there is associated a sheaf of Lie superalgebras, \(\mathfrak A\), and the first cohomology \(H^ 1(S,{\mathfrak A})\) with coefficients in that sheaf gives rise to a structure of a super Riemann surface on \(S\). The superalgebra of global sections of \(\mathfrak A\) has been considered earlier [\textit{K. Gawedzki}, Ann. Inst. Henri Poincaré, Sect. A 27 (1977), 355-366 (1978; Zbl 0369.53061)] as the algebra of graded vector fields on a certain holomorphic graded manifold associated to \(S\) in a natural way.