Abstract
We describe Hopf algebras which are central extensions of quantum current groups. For a special value of the central charge, we describe Casimir elements in these algebras. New types of generators for quantum current algebra and its central extension for quantum simple Lie groups, are obtained. The application of our construction to the elliptic case is also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
DrinfeldV. G.,Proceedings of the International Congress of Mathematicians, Berkeley, California, Vol. 1, Academic Press, New York, 1986, pp. 798–820.
JimboM.,Commun. Math. Phys. 102, 537–548 (1986).
Faddeev, L., Reshetikhin, N., and Takhtadjan, L., LOMI preprint, Leningrad, 1987.
Semenov-Tian-Shansky, M. A.,Publ. RIMS, Kyoto Univ. 21, No. 6 (1985).
Semenov-Tian-ShanskyM. A.,Funct. Anal. Appl. 17, 259–272 (1983).
Reshetikhin, N. Yu and Semenov-Tian-Shansky, M. A.,J. Geom. Phys. 5 (1988).
BelavinA. A. and DrinfeldV. G.,Funct. Anal. Appl. 16, 1–29 (1982) (in Russian).
KacV. G.,Infinite Dimensional Lie Algebras, Prog. in Math.44, Birkhäuser, Boston, 1983. Second edition, Cambridge Univ. Press, 1985.
KulishP. P., ReshetikhinN. Yu., and SklyaninE. K.,Lett. Math. Phys. 5, 393 (1981).