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Deformation of the Universal Enveloping Algebra of Γ (σ1, σ2, σ3)

Published online by Cambridge University Press:  20 November 2018

Yi Ming Zou
Yi Ming Zou*
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, MilwaukeeWI, USA 53201, e-mail: [email protected]
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Abstract

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The defining relations for the Lie superalgebra Γ (σ1, σ2, σ3) as a contragredient algebra are discussed and a PBW type basis theorem is proved for the corresponding q-deformation.

Keywords

16W3016S8022E70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 499 - 506
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Conway, J. B., Functions of one complex variable, GTM 11, Springer-Verlag, 1978.Google Scholar
2. Drinfeld, V. G., Quantum groups, Proc. ICM, Berkeley, 1986, 798–820.Google Scholar
3. Jimbo, M., A q-difference analogue of 11(g) and the Yang-Baxter equation, Lett. Math. Phys. 10(1985), 63–69.Google Scholar
4. Kac, V. G., Lie superalgebras, Adv. in Math. 26(1977), 8–96.Google Scholar
5. Floreanini, R., Leites, D. A. and Vinet, L., On the defining relations of quantum superalgebras, Lett. Math. Phys. 23(1991), 127–131.Google Scholar
6. Floreanini, R., Spiridonov, V. P. and Vinet, L., q-Oscillator realizations of the quantum superalgebras slq(m, n) and ospq(m, 2n), Comm. Math. Phys. 137(1991), 149–160.Google Scholar
7. Rosso, M., Finite dimensional representations of the quantum analogue of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys. 117(1988), 581–593.Google Scholar
8. Scheunert, M., The presentation and q deformation of special linear Lie superalgebras, J. Math. Phys. 34(1993), 3780–3808.Google Scholar
9. Zou, Y. M., Finite dimensional representations of Γ (σ1, σ2, σ3), J. Algebra (3)169(1994), 827–846.Google Scholar