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Abstract: Locally affine Lie algebras are generalizations of affine Kac-Moody algebraswith Cartan subalgebras of infinite rank whose root system is locally affine.In this note we study a class of representations of locally affine algebrasgeneralizing integrable highest weight modules. In particular, we constructsuch an integrable representation for each integral weight not vanishing on thecenter and show that, over the complex numbers, we thus obtain unitaryrepresentations w.r.t. a unitary real form.We also use Yoshii-s recent classification of locally affine root systems toderive a classification of so-called minimal locally affine Lie algebras andgive realizations as twisted loop algebras.



Author: Karl-Hermann Neeb

Source: https://arxiv.org/







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