Abstract
Let \(\mathfrak{g} = W_1 \) be the Witt algebra over an algebraically closed field k of characteristic p > 3; and let be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250: 473–484], we show that the variety is reducible, and not equidimensional. Irreducible components of and their dimensions are precisely given. As a consequence, the variety is not normal.
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Acknowledgements
The authors would like to express their thanks to the referees for many useful suggestions and comments on the manuscript. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11771279, 11801204) and the Natural Science Foundation of Shanghai (Grant No. 16ZR1415000).
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Yao, YF., Chang, H. Commuting variety of Witt algebra. Front. Math. China 13, 1179–1187 (2018). https://doi.org/10.1007/s11464-018-0725-9
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DOI: https://doi.org/10.1007/s11464-018-0725-9