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Graded Riemann surfaces and Krichever-Novikov algebras. (English) Zbl 0717.17001
Geometry and physics, Proc. 9th Winter Sch., SrnĂ­/Czech. 1989, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 22, 15-24 (1990).
[For the entire collection see Zbl 0699.00032.]
Krichever and Novikov introduced a series of quadratic algebras associated with Riemann surfaces. L. Bonora, M. Bregola, P. Cotta-Ramusino and M. Martellini [Phys. Lett. B 205, 53-56 (1988; see the following review)] generalized this construction to \(N=1\) extended super Riemann surfaces. Here the formulas of Bonora et al. for the central extension of Krichever-Novikov superalgebras are supposed to be corrected and the construction is performed in geometric terms (as well as in later papers by Bonora et al.)
Reviewer: D.Leites
MSC:
17A45 Quadratic algebras (but not quadratic Jordan algebras)
81R99 Groups and algebras in quantum theory
58A50 Supermanifolds and graded manifolds
30F99 Riemann surfaces
17A70 Superalgebras