Abstract
By considering the cohomology of the loop algebraL \(\mathcal{G}\), a representation ofL \(\mathcal{G}\) is constructed. the construction is based on a derivation δ ofL \(\mathcal{G}\) and a two-dimensional closed cochain ω ofl \(\mathcal{G}\) with coefficients in real numbersR 1. In the case of ω=0, the differential of the energy representation of the corresponding loop groupLG is derived.
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This work was supported in part by the National Natural Science Foundation of China.
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Dong, W.Z. The construction of a representation of loop algebras. Lett Math Phys 38, 377–388 (1996). https://doi.org/10.1007/BF01815520
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DOI: https://doi.org/10.1007/BF01815520