On Leibniz algebras, whose subideals are ideals
DOI:
https://doi.org/10.15407/dopovidi2017.09.015Keywords:
ideal, Leibniz algebra, subideal, T-algebraAbstract
We obtain a description of solvable Leibniz algebras, whose subideals are ideals. A description of certain types of Leibniz T-algebras is also obtained. In particular, it is established that the structure of Leibniz T-algebras essentially depends on the structure of its nil-radical.
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Bloh, A. M. (1965). On a generalization of the concept of Lie algebra. Dokl. AN SSSR, 165, pp. 471-473.
Bloh, A. M. (1967). Cartan — Eilenberg homology theory for a generalized class of Lie algebras. Dokl. AN SSSR, 175, pp. 824-826.
Bloh, A. M. (1971). A certain generalization of the concept of Lie algebra. Algebra and number theory. Uchenye Zapiski Moskov. Gos. Pedagog. Inst., 375, pp. 9-20 (in Russian).
Loday, J. L. (1993). Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Enseign. Math., 39, pp. 269-293.
Butterfield, J. & Pagonis, C. (1999). From Physics to Philosophy. Cambridge: Cambridge Univ. Press. https://doi.org/10.1017/CBO9780511597947
Dobrev, V. (Eds.) (2013). Lie theory and its applications in physics. IX International workshop. Tokyo: Springer. https://doi.org/10.1007/978-4-431-54270-4
Duplij, S. & Wess, J. (Ed.). (2001). Noncommutative Structures in Mathematics and Physics. NATO Science Series II. Vol. 22. Dordrecht: Kluwer. https://doi.org/10.1007/978-94-010-0836-5
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
Chupordya, V. A., Kurdachenko, L. A. & Subbotin, I. Ya. (2016). On some minimal Leibniz algebras. J. Algebra and Appl., 16, Iss. 5, 1750082, 16 p.
Stewart, I. N. (1969). Subideals of Lie algebras. Ph.D. Thesis, University of Warwick.
Gein, A. G. & Muhin, Yu. N. (1980). Complements to subalgebras of Lie algebras. Mat. Zapiski Ural. Gos. Univ., 12, pp. 24-48 (in Russian).
Amayo, R. K. & Stewart, I. (1974). Infinite-dimensional Lie algebras. Dordrecht: Springer. https://doi.org/10.1007/978-94-010-2305-4
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