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 S 0 of the Dirac theory of the Taub-NUT model, studied by Cotǎescu and Visinescu [J. Phys. A40, 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 H N, studied by Daboul and Slodowy, must be "twisted-like" (genuinely and not-genuinely twisted) KM subalgebras.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics