Geodesic
Colength of varieties of linear algebras
Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 553-559

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In this paper, an example of a variety of nonassociative algebras is constructed in which the system of Capelli identities of small rank is satisfied, whereas the colength function has exponential growth. As is well known, in the associative case and in the Lie case, the validity of Capelli identities implies the polynomial growth of the colength. 
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     author = {M. V. Zaicev and S. P. Mishchenko},
     title = {Colength of varieties of linear algebras},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a5/}
}
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M. V. Zaicev; S. P. Mishchenko. Colength of varieties of linear algebras. Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 553-559. http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a5/