Abstract
In defining quantum superalgebras, extra relations need to be added to the Serre-like relations. They are obtained for sl q (m, n) and osp q (m, 2n) usingq-oscillator representations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Drinfel'd, V. G., Quantum groups, inProceedings of the International Congress of Mathematicians, Berkeley (1986), vol. 1, Amer. Math. Soc., 1987, pp. 798–820.
Jimbo, M., Aq-difference analogue of U(g) and the Yang-Baxter equation,Lett. Math. Phys. 10, 63–69 (1985); Aq-analogue of U(gl(N+1)), Hecke algebra and the Yang-Baxter equation,ibid.11, 247–252 (1986).
Kac, V. G., private communication.
Leites, D. and Serganova, V., Defining relations for classical Lie superalgebras I, University of Stockholm-preprint, 1991, to appear inProc. Euler IMI Conference on Quantum Groups, Leningrad, 1990.
Chaichan, M. and Kulish, P., Quantum Lie superalgebras andq-oscillators,Phys. Lett. B234 72–80 (1990).
Floreanini, R., Spiridonov, V. P., and Vinet, L.,q-Oscillator realizations of the quantum superalgebras sl q (m, n) and osp q (m, 2n),Comm. Math. Phys. 137,149–160 (1991).
Kac, V. G., A sketch of Lie superalgebra theory,Comm. Math. Phys. 53, 31–64 (1977); Lie superalgebras,Adv. Math. 26, 8–96 (1977); Representations of classical Lie superalgebras, inLecture Notes in Mathematics 676, Springer-Verlag, Berlin, 1978, pp. 597–626.
Leites, D., Saveliev, M. V., and Serganova, V. V., Embeddings of osp(n/2) and the associated nonlinear supersymmetric equations, in M. A.Markov, V. I.Man'ko, and V. V.Dodonov (eds.),Group Theoretical Methods in Physics, vol. 1, VNU Science Press, Utrecht, 1986, pp. 255–297.
Rosso, M., An analogue of P.B.W. theorem and the universalR-matrix for U h sl(N+1).Comm. Math. Phys. 124, 307–318 (1989).
Biedenharn, L. C., The quantum group SU(2) q and aq-analogue of the boson operators,J. Phys. A22, L873-L878 (1989); MacFarlane, A. J., Onq-analogues of the quantum harmonic oscillator and the quantum group SU(2) q ,J. Phys. A22, 4581–4588 (1989); Hayashi, T., Q-analogue of Clifford and Weyl algebras-Sprinor and oscillator representations of quantum enveloping algebras,Comm. Math. Phys. 127, 129–144 (1990).
Egorov, G., How to superize gl(∞), to appear in J.Mickelsson (ed.),Proc. Topological and Geometrical Methods in Field Theory, Turku (Finland), World Scientific, Singagpore, 1991.
Leites, D., Clifford algebras and superalgebras and quantization,Theor. Math. Phys. 58, 150 (1984); Quantization and supermanifolds, supplement to F. Berezin and M. Shubin,Schrödinger Operator, Kluwer, Dordrecht, 1991.
Author information
Authors and Affiliations
Additional information
Supported in part by the National Sciences and Engineering Research Council (NSERC) of Canada.