Let $ \widetilde{\mathfrak{sv}} $ be the extended Schrödinger-Virasoro Lie algebra. In this paper, we consider the skew-symmetric biderivations of the extended Schrödinger-Virasoro Lie algebra. We prove that all biderivations of $ \widetilde{\mathfrak{sv}} $ are inner. Based on this result, we show that all linear commuting maps on $ \widetilde{\mathfrak{sv}} $, which have the form $ \psi(x) = \lambda x $, are standard.
Citation: Zhongxian Huang. Biderivations of the extended Schrödinger-Virasoro Lie algebra[J]. AIMS Mathematics, 2023, 8(12): 28808-28817. doi: 10.3934/math.20231476
Let $ \widetilde{\mathfrak{sv}} $ be the extended Schrödinger-Virasoro Lie algebra. In this paper, we consider the skew-symmetric biderivations of the extended Schrödinger-Virasoro Lie algebra. We prove that all biderivations of $ \widetilde{\mathfrak{sv}} $ are inner. Based on this result, we show that all linear commuting maps on $ \widetilde{\mathfrak{sv}} $, which have the form $ \psi(x) = \lambda x $, are standard.
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Zhongxian Huang. Biderivations of the extended Schrödinger-Virasoro Lie algebra[J]. AIMS Mathematics, 2023, 8(12): 28808-28817. doi: 10.3934/math.20231476
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