Abstract
We define the concepts of open Lie superalgebras and their closure and study their embedding into affine Kac–Moody (KM) superalgebras. We distinguish between two types of open algebras, whose closures typically yield twisted or untwisted KM superalgebras. We show that the open dynamical symmetry superalgebra S0 of the Dirac theory of the Taub–NUT model, studied by Cotăescu and Visinescu [J. Phys. A 40, 11987 (2007)], cannot be embedded into a twisted KM superalgebra, in contrast to their claim. Our analysis of the above relativistic model reveals the deeper reason of why the hydrogen algebras HN, studied by Daboul and Slodowy, must be “twisted-like” (genuinely and not-genuinely twisted) KM subalgebras.
Published Version
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