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Quasifinite highest weight modules over the super W 1+ algebra. (English) Zbl 0832.17026
The W 1+ algebra is a central extension of the Lie algebra of differential operators on the circle. Such algebras were studied and their quasifinite representations were classified by V. Kac and A. Radul [Commun. Math. Phys. 157, 429-457 (1993; Zbl 0826.17027)]. The authors extend these results to the super case. SW 1+ is a central extension of the Lie super algebra of super differential operators acting on the polynomial algebra over 2×2 super matrices. Again quasifiniteness is characterised by polynomials and the highest weights are expressed in terms of differential equations. As an example a (B,C)-system is considered.
MSC:
17B68Virasoro and related algebras
17B70Graded Lie (super)algebras
81T40Two-dimensional field theories, conformal field theories, etc.
81T60Supersymmetric field theories
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