Quantization and Cocycles on the Supertorus and Large-N Limits for the Classical Lie Superalgebras

E. S. Fradkin, V. Linetsky

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The Poisson superbracket Lie superalgebra on the supertorus T2d|N is considered and its quantization is carried out. It is shown that there exists a non-trivial supercentral extension by means of 2d arbitrary c-numbers (when N is even), or 2d Grassmann numbers (when N is odd). It is shown that the infinite-dimensional superalgebras on the supertorus T2d|N can be considered as certain generalizations and large-M limits of the classical superalgebras A(M| M) and Q(M) (when N is even and odd respectively).
Original languageEnglish
Pages (from-to)217-224
JournalModern Physics Letters A
StatePublished - 1991

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