Abstract
It was shown in an earlier paper that there is an Abelian extension \(\widehat{{\text{gl}}}_2 \) of the general linear algebra gl 2, that contains the current algebra with anomaly in 3+1 dimensions. We construct a three-parameter family of deformations \(\widetilde{{\text{gl}}}_2 (t)\) of \(\widehat{{\text{gl}}}_2 \). For certain choices of the deformation parameters, we can construct unitary representations. We also construct highest-weight nonunitary representations for all choices of the parameters.
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References
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This work was supported in part by U.S. Department of Energy Contract No. DE-AC02-76ER13065.