Geodesic
Yangian of the Strange Lie Superalgebra of $Q_{n-1}$ Type, Drinfel'd Approach
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Yangian of the strange Lie superalgebras in Drinfel'd realization is defined. The current system generators and defining relations are described.
Keywords: Yangian; strange Lie superalgebra; Drinfel'd realization; Hopf structure; twisted current bisuperalgebra. 
@article{SIGMA_2007_3_a68,
     author = {Vladimir Stukopin},
     title = {Yangian of the {Strange} {Lie} {Superalgebra} of $Q_{n-1}$ {Type,} {Drinfel'd} {Approach}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a68/}
}
TY  - JOUR
AU  - Vladimir Stukopin
TI  - Yangian of the Strange Lie Superalgebra of $Q_{n-1}$ Type, Drinfel'd Approach
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2007
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a68/
LA  - en
ID  - SIGMA_2007_3_a68
ER  - 
%0 Journal Article
%A Vladimir Stukopin
%T Yangian of the Strange Lie Superalgebra of $Q_{n-1}$ Type, Drinfel'd Approach
%J Symmetry, integrability and geometry: methods and applications
%D 2007
%V 3
%U http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a68/
%G en
%F SIGMA_2007_3_a68
Vladimir Stukopin. Yangian of the Strange Lie Superalgebra of $Q_{n-1}$ Type, Drinfel'd Approach. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a68/

[1] Drinfel'd V. G., “Quantum groups”, Proceedings of the International Congress of Mathematicians, Vol. 1, Berkley, 1988, 789–820 | MR

[2] Drinfel'd V. G., “Hopf algebras and the quantum Yang–Baxter equation”, Soviet Math. Dokl., 32 (1985), 254–258 | MR

[3] Drinfel'd V. G., “A new realization of Yangians and of quantum affine algebras”, Soviet Math. Dokl., 36 (1988), 212–216 | MR

[4] Molev A., “Yangians and their applications”, Handbook of Algebra, Vol. 3, North-Holland, Amsterdam, 2003, 907–959 ; math.QA/0211288 | MR

[5] Chari V., Pressley A., A guide to quantum groups, Camb. Univ. Press, Cambridge, 1995 | MR

[6] Zhang R. B., “Representations of super Yangian”, J. Math. Phys., 36 (1995), 3854–3865 ; hep-th/9411243 | DOI | MR | Zbl

[7] Zhang R. B., “The $\mathfrak{gl}(M,N)$ super Yangian and its finite-dimensional representations”, Lett. Math. Phys., 37 (1996), 419–434 ; q-alg/9507029 | DOI | MR | Zbl

[8] Zhang Y.-Z., “Super-Yangian double and its central extension”, Phys. Lett. A, 234 (1997), 20–26 ; q-alg/9703027 | DOI | MR | Zbl

[9] Crampe N., “Hopf structure of the Yangian $Y(sl_n)$ in the Drinfel'd realization”, J. Math. Phys., 45 (2004), 434–447 ; math.QA/0304254 | DOI | MR | Zbl

[10] Stukopin V., “Yangians of Lie superalgebras of type $A(m,n)$”, Funct. Anal. Appl., 28:3 (1994), 217–219 | DOI | MR | Zbl

[11] Stukopin V., “Representation theory and doubles of Yangians of classical Lie superalgebras”, Asymptotic Combinatorics with Application to Mathematical Physics (2001, St. Petersburg), NATO Sci. Ser. II Math. Phys. Chem., 77, Kluwer Acad. Publ., Dordrecht, 2002, 255–265 | MR | Zbl

[12] Stukopin V., “Yangians of classical Lie superalgebras: basic constructions, quantum double and universal $R$-matrix”, Proceedings of Fourth International Conference “Symmetry in Nonlinear Mathematical Physics” (July 9–15, 2003, Kyiv), Proceedings of Institute of Mathematics, Kyiv, 50, no. 3, eds. A. G. Nikitin, V. M. Boyko, R. O. Popovych and I. A. Yehorchenko, 2004, 1196–1201 | MR

[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 | DOI | MR | Zbl

[15] Nazarov M., “Yangian of the queer Lie superalgebra”, Comm. Math. Phys., 208 (1999), 195–223 ; math.QA/9902146 | DOI | MR | Zbl

[16] Kac V., “A sketch of Lie superalgebra theory”, Comm. Math. Phys., 53 (1977), 31–64 | DOI | MR | Zbl

[17] Frappat L., Sciarrino A., Sorba P., Dictionary on Lie superalgebras, Academic Press, Inc., San Diego, CA, 2000 | MR

[18] Leites D., Serganova V., “Solutions of the classical Yang–Baxter equations for simple Lie superalgebras”, Theoret. and Math. Phys., 58:1 (1984), 16–24 | DOI | MR | Zbl