Geodesic
Affine modular Lie algebras
Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 573-586 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to the construction of affine Kac–Moody algebras via defining relations arising from an integral affine Cartan matrix, in the case where the ground field has positive characteristic $p>7$. Explicit constructions are given for algebras obtained in this way; in distinction with the zero characteristic case they have infinite-dimensional center. A theorem on the universality of this central extension is proved, and a series of finite-dimensional factors of affine modular algebras over the ideals having trivial intersection with Cartan's subalgebra is constructed. Moreover, a construction for the PI-envelopes of affine Kac–Moody algebras is given. 
@article{SM_1991_70_2_a13,
     author = {Yu. V. Billing},
     title = {Affine modular {Lie} algebras},
     journal = {Sbornik. Mathematics},
     pages = {573--586},
     year = {1991},
     volume = {70},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_70_2_a13/}
}
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Yu. V. Billing. Affine modular Lie algebras. Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 573-586. http://geodesic.mathdoc.fr/item/SM_1991_70_2_a13/

[1] Kac V. G., Infinite dimensional Lie algebras, Boston, 1983 | MR

[2] Seligman G. M., Modular Lie algebras, Berlin, 1967 | MR

[3] Wilson R. L., “Euclidean Lie algebras are universal central extensions”, Lecture Notes in Math., 933 (1982), 210–213 | DOI | MR | Zbl

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

[5] Billig Yu. V., “O gomomorfnom obraze spetsialnoi algebry Li”, Matem. sb., 136(178) (1988), 320–323 | MR | Zbl

[6] Shirshov A. I., “O svobodnykh koltsakh Li”, Matem. sb., 45(87) (1958), 113–122 | Zbl