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Orthosymplectic quantum function superalgebras OSP q (2l+1|2n)

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Abstract

By the R-matrix of orthosymplectic quantum superalgebra U q (osp(2l+1|2n)) in the vector representation, we establish the corresponding quantum Hopf superalgebra OSP q (2l + 1|2n). Furthermore, it is shown that OSP q (2l + 1|2n) is coquasitriangular.

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References

  1. Reshetikhin, N. Yu., Takhtadzhyan, L. A., Faddeev, L. D.: Quantization of lie groups and lie algebras. Algebra Analize, 1, 178–206 (1989); English translation: Leningrad Math. J., 1, 193–225 (1990)

    MathSciNet  Google Scholar 

  2. Scheunert, M.: The quantum supergroup SPOq(2n|2m) and an SPOq(2n|2m)-covariant quantum Weyl superalgebra, preprint, BONN-TH-2000-03

  3. Lee, H. C., Zhang, R. B.: Geometry and representations of the quantum supergroup OSPq(1|2n). J. Math. Phys., 40, 3175–3190 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Zhang, R. B.: Structure and representations of the quantum supergroup OSPq(2|2n). J. Math. Phys., 41, 6639–6656 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Manin, Yu. I.: Multiparametric quantum deformation of the general linear supergroup. Commun. Math. Phys., 123, 163–175 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  6. Zhang, R. B.: Structure and representations of the quantum general linear supergroup. Commun. Math. Phys., 195, 525–547 (1998)

    Article  MATH  Google Scholar 

  7. Boseck, H.: Classical Lie supergroups. Math. Nachr., 148, 81–115 (1990)

    MATH  MathSciNet  Google Scholar 

  8. Boseck, H.: Affine Lie supergroups. Math. Nachr., 143, 303–327 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Scheunert, M.: The R-matrix of the symplecto-orthogonal quantum superalgebra U q(spo(2n|2m)) in the vector representation, preprint, BONN-TH-2000-03

  10. Kac, V. G.: Lie superalgebras. Adv. Math., 26, 8–96 (1977)

    Article  MATH  Google Scholar 

  11. Kac, V. G.: Representations of classical Lie superalgebras, Lecture Notes in Math., Vol. 676, Springer-Verlag, Berlin, 1978, 597–626

    Google Scholar 

  12. Kac, V. G.: A sketch of Lie superalgebras Theory. Comm. Math. Phys., 53, 31–64 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  13. Drinfeld, V. G.: Quantum groups. Proc. Int. Cong. Math. Berkeley, 1, 789–820 (1986)

    Google Scholar 

  14. Scheunert, M.: Eigenvalues of Casimir operators for the general linear, the special linear, and the orthosymplectic Lie superalgebras. J. Math. Phys., 24, 2681–2688 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  15. Scheunert, M.: Graded tensor calculus. J. Math. Phys., 24, 2658–2670 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  16. Blumen, S. C.: The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U q(osp(1|2n)). arXiv: math. QA/0607049 vl 3 Jul 2006

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Correspondence to Shi Lin Yang.

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Supported by National Natural Science Foundation of China (Grant Nos. 10671016, 10771014) and Foundation of Selected Excellent Science and Technology Activity for Returned Scholars of Beijing 1)

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Liu, J.L., Yang, S.L. Orthosymplectic quantum function superalgebras OSP q (2l+1|2n). Acta. Math. Sin.-English Ser. 27, 983–1004 (2011). https://doi.org/10.1007/s10114-011-8037-y

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  • DOI: https://doi.org/10.1007/s10114-011-8037-y

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