Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 069, 12 pages      arXiv:0705.3250      http://dx.doi.org/10.3842/SIGMA.2007.069
Contribution to the Vadim Kuznetsov Memorial Issue

Yangian of the Strange Lie Superalgebra of Qn-1 Type, Drinfel'd Approach

Vladimir Stukopin
Don State Technical University, 1 Gagarin Square, Rostov-na-Donu, 344010 Russia

Received November 01, 2006, in final form May 06, 2007; Published online May 22, 2007

Abstract
The Yangian of the strange Lie superalgebras in Drinfel'd realization is defined. The current system generators and defining relations are described.

Key words: Yangian; strange Lie superalgebra; Drinfel'd realization; Hopf structure; twisted current bisuperalgebra.

pdf (237 kb)   ps (182 kb)   tex (15 kb)

References

  1. Drinfel'd V.G., Quantum groups, in Proceedings of the International Congress of Mathematicians, Vol. 1, Berkley, 1988, 789-820.
  2. Drinfel'd V.G., Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl. 32 (1985), 254-258.
  3. Drinfel'd V.G., A new realization of Yangians and of quantum affine algebras, Soviet Math. Dokl. 36 (1988), 212-216.
  4. Molev A., Yangians and their applications, in Handbook of Algebra, Vol. 3, North-Holland, Amsterdam, 2003, 907-959, math.QA/0211288.
  5. Chari V., Pressley A., A guide to quantum groups, Camb. Univ. Press, Cambridge, 1995.
  6. Zhang R.B., Representations of super Yangian, J. Math. Phys. 36 (1995), 3854-3865, hep-th/9411243.
  7. Zhang R.B., The gl(M,N) super Yangian and its finite-dimensional representations, Lett. Math. Phys. 37 (1996), 419-434, q-alg/9507029.
  8. Zhang Y.-Z., Super-Yangian double and its central extension, Phys. Lett. A 234 (1997), 20-26, q-alg/9703027.
  9. Crampe N., Hopf structure of the Yangian Y(sln) in the Drinfel'd realization, J. Math. Phys. 45 (2004), 434-447, math.QA/0304254.
  10. Stukopin V., Yangians of Lie superalgebras of type A(m,n), Funct. Anal. Appl. 28 (1994), 217-219.
  11. Stukopin V., Representation theory and doubles of Yangians of classical Lie superalgebras, in Asymptotic Combinatorics with Application to Mathematical Physics (2001, St. Petersburg), NATO Sci. Ser. II Math. Phys. Chem., Vol. 77, Kluwer Acad. Publ., Dordrecht, 2002, 255-265.
  12. Stukopin V., Yangians of classical Lie superalgebras: basic constructions, quantum double and universal R-matrix, in Proceedings of Fourth International Conference "Symmetry in Nonlinear Mathematical Physics" (July 9-15, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko, Proceedings of Institute of Mathematics, Kyiv 50 (2004), Part 3, 1196-1201.
  13. Stukopin V., Quantum double of Yangian of Lie superalgebra A(m,n) and computation of universal R-matrix, math.QA/0504302.
  14. Nazarov M., Quantum Berezinian and the classical Capelly identity, Lett. Math. Phys. 21 (1991), 123-131.
  15. Nazarov M., Yangian of the queer Lie superalgebra, Comm. Math. Phys. 208 (1999), 195-223, math.QA/9902146.
  16. Kac V., A sketch of Lie superalgebra theory, Comm. Math. Phys. 53 (1977), 31-64.
  17. Frappat L., Sciarrino A., Sorba P., Dictionary on Lie superalgebras, Academic Press, Inc., San Diego, CA, 2000.
  18. Leites D., Serganova V., Solutions of the classical Yang-Baxter equations for simple Lie superalgebras, Theoret. and Math. Phys. 58 (1984), 16-24.

Previous article   Next article   Contents of Volume 3 (2007)