Lie super-bialgebra and quantization of the super Virasoro algebra (Q2814229)

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scientific article; zbMATH DE number 6595471
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Lie super-bialgebra and quantization of the super Virasoro algebra
scientific article; zbMATH DE number 6595471

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    Lie super-bialgebra and quantization of the super Virasoro algebra (English)
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    20 June 2016
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    Lie super-bialgebra
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    super Virasoro algebra
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    Drinfel'd twist quantization
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    In this paper, the authors show that all Lie super-bialgebra structures on the super Virasoro algebra, whose even part is the centerless twisted Heisenberg-Virasoro algebra, are triangular coboundary; the proof of this result relies on results of the paper [\textit{D. Liu} et al., J. Algebra 359, 35--48 (2012; Zbl 1316.17014)], where the analogous result is shown for the centerless twisted Heisenberg-Virasoro algebra. This is in turn related to previous analogous results of \textit{S.-H. Ng} and \textit{E. J. Taft}, who showed in [J. Pure Appl. Algebra 151, No. 1, 67--88 (2000; Zbl 0971.17008)] that all Lie bialgebra structures on the centerless Virasoro algebra and the Virasoro algebra are triangular coboundary. The authors also obtain, by means of Drinfel'd twist quantization, explicit quantizations of the Lie super-bialgebra structures on the super Virasoro algebra.
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