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DJKM algebras. I: Their universal central extension. (English) Zbl 1269.17009

In this paper the authors give an explicit description, in terms of generators and relations, of the (four dimensional) universal central extension of the infinite dimensional Lie algebra \(\mathfrak{g}\otimes\mathbb{C}[t,t^{-1},u| u^2=(t^2-b^2)(t^2-c^2)]\), where \(b\neq \pm c\) are complex constants and \(\mathfrak{g}\) is a simple finite dimensional complex Lie algebra.

MSC:

17B65 Infinite-dimensional Lie (super)algebras
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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