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\(n\)-Lie algebras. (English) Zbl 0594.17002
Translation from Sib. Mat. Zh. 26, No. 6(154), 126–140 (Russian) (1985; Zbl 0585.17002).

MSC:
17A42 Other \(n\)-ary compositions \((n \ge 3)\)
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
17A65 Radical theory (nonassociative rings and algebras)
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
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References:
[1] A. G. Kurosh, ?Free sums of multioperator algebras,? Sib. Mat. Zh., No. 1, 62-70 (1960). · Zbl 0096.25304
[2] A. G. Kurosh, ?Multioperator rings and algebras,? Usp. Mat. Nauk,24, No. 1, 3-15 (1969). · Zbl 0204.35701
[3] T. M. Baranovich and M. S. Burgin, ?Linear ?-algebras,? Usp. Mat. Nauk,30, No. 4, 61-106 (1975).
[4] B. A. Rozenfel’d, Spaces of Higher Dimensions [in Russian], Nauka, Moscow (1966).
[5] N. V. Efimov and E. R. Rozenforn, Linear Algebra and Multidimensional Geometry [in Russian], Nauka, Moscow (1974).
[6] A. G. Kurosh, Lectures in General Algebra [in Russian], Nauka, Moscow (1973). · Zbl 0271.08001
[7] N. Jacobson, Lie Algebras [Russian translation], Mir, Moscow (1969). · Zbl 0253.17013
[8] M. Goto and F. Grosshans, Semisimple Lie Algebras [Russian translation], Mir, Moscow (1981). · Zbl 0528.17001
[9] V. T. Filippov, ?On one generalization of Lie algebras,? Preprint No. 64, Mathematics Inst., Siberian Branch, Acad. Sci. of the USSR, Novosibirsk (1984).
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