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Frontiers of Mathematics in China

, Volume 13, Issue 5, pp 1179–1187 | Cite as

Commuting variety of Witt algebra

  • Yu-Feng Yao
  • Hao Chang
Research Article

Abstract

Let \(\mathfrak{g} = W_1 \) be the Witt algebra over an algebraically closed field k of characteristic p > 3; and let Open image in new window 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 Open image in new window is reducible, and not equidimensional. Irreducible components of Open image in new window and their dimensions are precisely given. As a consequence, the variety Open image in new window is not normal.

Keywords

Witt algebra irreducible component dimension commuting variety 

MSC

17B05 17B50 17B70 

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Notes

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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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiChina
  2. 2.School of Mathematics and StatisticsCentral China Normal UniversityWuhanChina

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