Embedding of "open" superalgebras into affine Kac-Moody superalgebras

Claudia Daboul; Jamil Daboul; Marc de Montigny

doi:10.1063/1.3371219

Embedding of "open" superalgebras into affine Kac-Moody superalgebras

Claudia Daboul, Jamil Daboul, Marc de Montigny

Department of Physics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 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.

Original language	English
Article number	009004JMP
Journal	Journal of Mathematical Physics
Volume	51
Issue number	5
DOIs	https://doi.org/10.1063/1.3371219
State	Published - 1 May 2010

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3371219

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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 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.",

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AB - 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.

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Embedding of "open" superalgebras into affine Kac-Moody superalgebras

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