Varieties of affine Kac-Moody algebras |
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Authors: | M. V. Zaitsev |
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Affiliation: | (1) M. V. Lomonosov Moscow State University, Moscow, USSR |
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Abstract: | 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. Translated fromMatematicheskie Zametki, Vol. 62 No. 1, pp. 95–102, July 1997. Translated by A. I. Shtern |
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Keywords: | variety of algebras affine Kac-Moody algebra identity growth of a variety twisted affine Kac-Moody algebra |
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