On structure and TKK algebras for Jordan superalgebras |
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Authors: | Sigiswald Barbier Kevin Coulembier |
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Institution: | 1. Faculty of Engineering and Architecture, Department of Mathematical Analysis, Ghent University, Ghent, Belgium;2. School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales, Australia |
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Abstract: | We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate that, for unital superalgebras, all the definitions of the structure algebra and the TKK constructions reduce to one of two cases. Moreover, one can be obtained as the Lie superalgebra of superderivations of the other. We also show that, for non-unital superalgebras, more definitions become nonequivalent. As an application, we obtain the corresponding Lie superalgebras for all simple finite dimensional Jordan superalgebras over an algebraically closed field of characteristic zero. |
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Keywords: | Lie superalgebras Jordan superalgebras TKK-construction |
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