Geodesic
Varieties of affine Kac--Moody algebras
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 95-102.

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In this paper the identities of the complex affine Kac–Moody algebras are studied. It is proved that the identities of twisted affine algebras coincide with those of the corresponding nontwisted algebras. Moreover, in the class of nontwisted affine Kac–Moody algebras, each of these algebras is uniquely defined by its identities. It is shown that the varieties of affine algebras, as well as the varieties defined by finitely generated three-step solvable Lie algebras, have exponential growth. 
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M. V. Zaicev. Varieties of affine Kac--Moody algebras. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 95-102. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a9/

[1] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1985 | Zbl

[2] Kats V., Beskonechnomernye algebry Li, Mir, M., 1993 | Zbl

[3] Billig Yu. V., “O gomomorfnom obraze spetsialnoi algebry Li”, Matem. sb., 136:7 (1988), 320–323 | Zbl

[4] Mischenko S. P., “Standartnoe lievo tozhdestvo v razreshimykh mnogoobraziyakh assotsiativnogo tipa”, Vestn. MGU. Ser. 1. Matem., mekh., 1995, no. 4, 30–36 | Zbl

[5] Mischenko S. P., “Rost mnogoobrazii algebr Li”, UMN, 45:6 (1990), 25–45 | Zbl

[6] Zaitsev M. V., “Tozhdestva affinnykh algebr Katsa–Mudi”, Vestn. MGU. Ser. 1. Matem., mekh., 1996, no. 2, 33–36 | MR

[7] Kushkulei A. Kh., Razmyslov Yu. P., “Mnogoobraziya, porozhdennye neprivodimymi predstavleniyami algebr”, Vestn. MGU. Ser. 1. Matem., mekh., 1983, no. 5, 4–7 | MR