Central extensions of quantum current groups. (English) Zbl 0692.22011

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


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
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