On Defining Relations of Affine Lie Superalgebras and Affine Quantized Universal Enveloping Superalgebras

Publications of the Research Institute for Mathematical Sciences

Volumn 35, Issue 3, 1999, Pages 321-390

  Yamane, Hiroyuki ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039172450     PISSN: 00345318     EISSN: None     Source Type: Journal    
DOI: 10.2977/prims/1195143607     Document Type: Article

References (21)

1. Beck, J., Braid group action and quantum affine algebras, Comm. Math. Phys., 165 (1994), 555–568.
2. Drinfeld, V.G., Quantum groups, in Proc. Int. Congr. Math., Berkeley, 1986, Amer. Math. Soc., (1988), 798–820.
3. Drinfeld, V.G., On almost commutative Hopf algebras, Leningrad Math. J., 1 (1990), 321–342.
4. Drinfeld, V.G., New realizations of Yangian and quantum affine algebra, Sov. Math. Doklady, 36 (1988), 212–216.
5. Frappet, L., Seiarino, A., and Sorba, P., Structure of basic Lie superalgebras and of their affine extensions, Comm. Math. Phys., 121 (1989), 457–500.
6. Gabber, O. and Kac, V.G., On defining relations of certain infinitedimensional Lie algebras, Bull. Amer. Math. Soc., 5 (1981), 185–189.
7. Iwahori, N. and Matsumoto, H., On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. IHES, 25 (1965), 5–48.
8. Jimbo, M., A q-defference analogue of U(G) and the Yang-Baxter equation, Lett. Math. Phys., 10 (1985), 798–820.
9. Kac, V.G., Infinite dimensional Lie algebras, 3rd ed., Cambridge Univ. Press, Cambridge, 1990.
10. Kac, V.G., Lie superalgebras, Adv. Math., 26 (1977), 8–96.
11. Khoroshkin, S.M. and Tolstoy, V.N., Twisting of quantum (super-) algebras, in Generalized symmetries in physics (Claustal, 1993), World Sci. Publishing, River Edge, NJ, (1994), 42–54.
12. Lusztig, G., Introduction to Quantum Groups, Birkhauser, 1993.
13. Lusztig, G., Affine Hecke algebras and their graded version, Journal of AMS, 2 (1989), 599–625.
14. Leites, D., and Serganova, V., Defining relations for classical Lie superalgebras I, in Proc. Topological and Geometrical Methods in Field Theory, World Sci., Singapore, (1992), 194-201.
15. Leites, D., Saveliev, M., and Serganova, V., Embeddings of Lie superalgebra osp (1, 2) and nonlinear symmetric equations, in Group-theoretical methods in Physics, Proceedings of the Third Yurmala Seminar (Yurmala, 1995), Moscow, 1986, 255–298.
16. Rosso, M., Finite dimensional representations of the quantum analog of a complex simple Lie algebra, Comm. Math. Phys., 117 (1988), 581–593.
17. Van De Leur, J.W., Contragredient Lie superalgebras of finite growth, Thesis, University of Utrecht, 1986.
18. Van De Leur, J.W., A classification of contragredient Lie superalgebras of finite growth, Comm. Algebra, 17 (1989), 1815–1842.
19. Serganova, V., Automorphisms of simple Lie superalgebras, Math USSR-Izv., 24 (1984), 539–551.
20. Yamane, H., Quantized enveloping algebras associated to simple Lie superalgebras and their universal R-matrices, Publ. RIMS, Kyoto Univ., 30 (1994), 15–87.
21. Yamane, H., A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras, Proc. Japan Acad., 70A (1994), 31–36.