In this paper, we give for each affinisation g of a simple Hilbert-Lie algebra k an explicit isomorphism from g to one of the standard affinisations of k. The existence of such an isomorphism could also be derived from the classification of locally affine root systems, but for representation theoretic purposes it is crucial to obtain it explicitely as a deformation between two twists which is compatible with the root decompositions. We illustrate this by applying our isomorphism theorem to the study of positive energy highest weight representations of g.

In subsequent work, the present paper will be used to obtain a complete classification of the positive energy highest weight representations of affinisations of}, author = {Marquis, TimothÃ©e and Neeb, Karl-Hermann}, doi = {10.4153/CJM-2016-003-x}, faupublication = {yes}, journal = {Canadian Journal of Mathematics-Journal Canadien De Mathematiques}, peerreviewed = {Yes}, title = {{Isomorphisms} of twisted {Hilbert} loop algebras}, url = {https://arxiv.org/abs/1508.07938}, year = {2017} }