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Lowest-energy representations of non-centrally extended diffeomorphism algebras. (English) Zbl 0936.17025
Author’s abstract: We describe a class of non-central extensions of the diffeomorphism algebra in $$N$$-dimensional spacetime, and construct lowest-energy modules thereof, thus generalizing work of Eswara Rao and Moody. There is one representation for each representation of $$\text{Vir }\widetilde {\ltimes}_{k_0} \widehat{\text{gl}(N)}$$ (an extension of the semi-direct product). Similar modules are constructed for gauge algebras.

##### MSC:
 17B68 Virasoro and related algebras 17B66 Lie algebras of vector fields and related (super) algebras 17B81 Applications of Lie (super)algebras to physics, etc.
##### Keywords:
roots; parabolic sets; closed sets; Kac-Moody algebra
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