On the structure of Leibniz algebras, whose subalgebras are ideals or core-free
DOI:
https://doi.org/10.15407/dopovidi2020.07.017Keywords:
core-free subalgebras, extraspecial algebra, ideal, Leibniz algebra, Lie algebra, monolithic algebraAbstract
An algebra L over a field F is said to be a Leibniz algebra (more precisely, a left Leibniz algebra), if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] — [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras. A subalgebra S of a Leibniz algebra L is called core-free, if S does not include the non-zero ideal. We study the Leibniz algebras, whose subalgebras are either ideals or core-free.
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Blokh, A. (1965). A generalization of the concept of a Lie algebra. Dokl. AN SSSR, 165, No. 3, pp. 471-473 (in Russian).
Blokh, A. (1967). Cartan–Eilenberg homology theory for a generalized class of Lie algebras. Dokl. AN SSSR, 175, No. 2, pp. 266-268 (in Russian).
Blokh, A. M. (1971). A certain generalization of the concept of Lie algebra. Uchenye zapiski Moskov. Gos. Pedagog. Inst., 375, pp. 9-20 (in Russian).
Loday, J. L. (1993). Une version non commutative des algebres de Lie: les algèbres de Leibniz. Enseign. Math., 39, pp. 269-293. https://doi.org/10.5169/seals-60428
Loday, J. L. (1998). Cyclic homology. Grundlehren der Mathematischen Wissenschaften, Vol. 301. 2nd ed. Berlin: Springer. https://doi.org/10.1007/978-3-662-11389-9
Chupordya, V. A., Kurdachenko, L. A. & Subbotin, I. Ya. (2017). On some “minimal” Leibniz algebras. J. Algebra Appl., 16, 1750082. https://doi.org/10.1142/S0219498817500827
Kurdachenko, L. A., Semko, N. N. & Subbotin, I. Ya. (2017). The Leibniz algebras whose subalgebras are ideals. Open Math., 15, pp. 92-100. https://doi.org/10.1515/math-2017-0010
Kurdachenko, L. A., Semko, N. N. & Subbotin, I. Ya. (2017). Leibniz algebras, whose all subalgebras are ideals. Dopov. Nac. akad. nauk. Ukr., No. 6, pp. 9-13. https://doi.org/10.15407/dopovidi2017.06.009
Kurdachenko, L. A., Otal, J. & Pypka, A. A. (2016). Relationships between factors of canonical central series of Leibniz algebras. European J. Math., 2, pp. 565-577. https://doi.org/10.1007/s40879-016-0093-5
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