Table of Contents
ISRN Mathematical Physics
Volume 2013, Article ID 672872, 13 pages
http://dx.doi.org/10.1155/2013/672872
Research Article

Quasifinite Representations of Classical Subalgebras of the Lie Superalgebra of Quantum Pseudodifferential Operators

Famaf-Ciem, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina

Received 11 June 2013; Accepted 5 July 2013

Academic Editors: A. M. Gavrilik, M. Martins, and K. Netocny

Copyright © 2013 José I. García and José I. Liberati. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We classify the anti-involutions of the superalgebra of quantum pseudodifferential operators on the super circle preserving the principal gradation, producing in this way a family of Lie subalgebras minus fixed by these anti-involutions. We classify the irreducible quasifinite highest weight representations of the central extension of these Lie subalgebras.