Geodesic
New example of a variety of lie algebras with fractional exponent
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 44-47 
S. S. Mishchenko. New example of a variety of lie algebras with fractional exponent. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 44-47. http://geodesic.mathdoc.fr/item/VMUMM_2011_6_a9/
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     author = {S. S. Mishchenko},
     title = {New example of a variety of lie algebras with fractional exponent},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {44--47},
     year = {2011},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_6_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the case of characteristic zero, the variety generated by a simple infinite-dimensional Lie algebra of Cartan type $W_2$ has a fractional exponent.