Commuting variety of Witt algebra

doi:10.1007/s11464-018-0725-9

Front. Math. China

2018, Vol. 13

Issue (5) : 1179-1187 https://doi.org/10.1007/s11464-018-0725-9

RESEARCH ARTICLE

Commuting variety of Witt algebra

Yu-Feng YAO¹, Hao CHANG²(

)

¹. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
². School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

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Abstract

Let g= W₁ be the Witt algebra over an algebraically closed field k of characteristic p >3, and let $C (g)$ = {(x, y) ∈g ×g | [x, y] = 0}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 $C (g)$ is reducible, and not equidimensional. Irreducible components of $C (g)$ and their dimensions are precisely given. As a consequence, the variety $C (g)$ is not normal.

Keywords Witt algebra irreducible component dimension commuting variety

Corresponding Author(s): Hao CHANG

Issue Date: 29 October 2018

Cite this article:

Yu-Feng YAO,Hao CHANG. Commuting variety of Witt algebra[J]. Front. Math. China, 2018, 13(5): 1179-1187.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0725-9
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I5/1179

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