Reshetikhin, N. Yu.; Semenov-Tian-Shansky, Michael A. Central extensions of quantum current groups. (English) Zbl 0692.22011 Lett. Math. Phys. 19, No. 2, 133-142 (1990). The central extensions of quantum current groups are described. They are the central extensions of noncommutative and noncocommutative Hopf algebras which provide the deformations of the enveloping algebras of affine Lie algebras. For a special value of the central charge the Casimir elements in these algebras are described. From the physicist’s point of view the construction carried out in the paper may be considered as the construction of Schwinger terms for a quantum current algebra. Reviewer: P.Maślanka Cited in 5 ReviewsCited in 94 Documents MSC: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties 17B65 Infinite-dimensional Lie (super)algebras 16S80 Deformations of associative rings 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 17B55 Homological methods in Lie (super)algebras Keywords:central extensions; quantum current groups; noncocommutative Hopf algebras; deformations; enveloping algebras of affine Lie algebras; central charge; Casimir elements; Schwinger terms; quantum current algebra PDFBibTeX XMLCite \textit{N. Yu. Reshetikhin} and \textit{M. A. Semenov-Tian-Shansky}, Lett. Math. Phys. 19, No. 2, 133--142 (1990; Zbl 0692.22011) Full Text: DOI References: [1] DrinfeldV. G.,Proceedings of the International Congress of Mathematicians, Berkeley, California, Vol. 1, Academic Press, New York, 1986, pp. 798-820. [2] JimboM.,Commun. Math. Phys. 102, 537-548 (1986). · Zbl 0604.58013 · doi:10.1007/BF01221646 [3] Faddeev, L., Reshetikhin, N., and Takhtadjan, L., LOMI preprint, Leningrad, 1987. [4] Semenov-Tian-Shansky, M. A.,Publ. RIMS, Kyoto Univ. 21, No. 6 (1985). [5] Semenov-Tian-ShanskyM. A.,Funct. Anal. Appl. 17, 259-272 (1983). · Zbl 0535.58031 · doi:10.1007/BF01076717 [6] Reshetikhin, N. Yu and Semenov-Tian-Shansky, M. A.,J. Geom. Phys. 5 (1988). [7] BelavinA. A. and DrinfeldV. G.,Funct. Anal. Appl. 16, 1-29 (1982) (in Russian). · Zbl 0498.32010 · doi:10.1007/BF01081801 [8] KacV. G.,Infinite Dimensional Lie Algebras, Prog. in Math.44, Birkhäuser, Boston, 1983. Second edition, Cambridge Univ. Press, 1985. [9] KulishP. P., ReshetikhinN. Yu., and SklyaninE. K.,Lett. Math. Phys. 5, 393 (1981). · Zbl 0502.35074 · doi:10.1007/BF02285311 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.