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Keywords:
Leibniz algebra; Lie algebra; ideal; cyclic Leibniz algebra; derivation
Summary:
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
References:
[1] Ayupov Sh., Omirov B., Rakhimov I.: Leibniz Algebras: Structure and Classification. CRC Press, Boca Raton, 2020.
[2] Batten Ray Ch., Combs A., Gin N., Hedges A., Hird J. T., Zack L.: Nilpotent Lie and Leibniz algebras. Comm. Algebra 42 (2014), no. 6, 2404–2410. DOI 10.1080/00927872.2012.717655 | MR 3169714
[3] Berkovich Ya.: Groups of Prime Power Order. Vol. 1. De Gruyter Expositions in Mathematics, 46, Walter de Gruyter GmbH & Co. KG, Berlin, 2008. MR 2464640
[4] Bloh A. M.: On a generalization of the concept of Lie algebra. Dokl. Akad. Nauk SSSR 165 (1965), 471–473 (Russian). MR 0193114
[5] Chupordia V. A., Kurdachenko L. A., Semko N. N.: On the structure of Leibniz algebras, whose subalgebras are ideals or core-free. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki (2020), no. 7, 17–21. DOI 10.15407/dopovidi2020.07.017 | MR 4169625
[6] Chupordia V. A., Kurdachenko L. A., Subbotin I. Ya.: On some “minimal" Leibniz algebras. J. Algebra Appl. 16 (2017), no. 5, 1750082, 16 pages. DOI 10.1142/S0219498817500827 | MR 3634087
[7] Kirichenko V. V., Kurdachenko L. A., Pypka A. A., Subbotin I. Ya.: Some aspects of Leibniz algebra theory. Algebra Discrete Math. 24 (2017), no. 1, 1–33. MR 3711054
[8] Kurdachenko L. A., Otal J., Pypka A. A.: Relationships between factors of canonical central series of Leibniz algebras. Eur. J. Math. 2 (2016), no. 2, 565–577. DOI 10.1007/s40879-016-0093-5 | MR 3499000
[9] Kurdachenko L. A., Otal J., Subbotin I. Ya.: On some properties of the upper central series in Leibniz algebras. Comment. Math. Univ. Carolin. 60 (2019), no. 2, 161–175. MR 3982464
[10] Kurdachenko L. A., Semko N. N., Subbotin I. Ya.: The Leibniz algebras whose subalgebras are ideals. Open Math. 15 (2017), no. 1, 92–100. DOI 10.1515/math-2017-0010 | MR 3613335
[11] Kurdachenko L. A., Semko N. N., Subbotin I. Ya.: On the anticommutativity in Leibniz algebras. Algebra Discrete Math. 26 (2018), no. 1, 97–109. MR 3877183
[12] Kurdachenko L. A., Semko N. N., Subbotin I. Ya.: Applying group theory philosophy to Leibniz algebras: some new developments. Adv. Group Theory Appl. 9 (2020), 71–121. MR 4123458
[13] Kurdachenko L. A., Subbotin I. Ya., Semko N. N.: From groups to Leibniz algebras: common approaches, parallel results. Adv. Group Theory Appl. 5 (2018), 1–31. MR 3824446
[14] Kurdachenko L. A., Subbotin I. Ya., Yashchuk V. S.: Leibniz algebras whose subideals are ideals. J. Algebra Appl. 17 (2018), no. 8, 1850151, 15 pages. MR 3825312
[15] Kurdachenko L. A., Subbotin I. Ya., Yashchuk V. S.: Leibniz algebras whose subalgebras are left ideals. Serdica Math. J. 46 (2020), no. 2, 175–194. MR 4154030
[16] Kurdachenko L. A., Subbotin I. Ya., Yashchuk V. S.: Some antipodes of ideals in Leibniz algebras. J. Algebra Appl. 19 (2020), no. 6, 2050113, 14 pages. DOI 10.1142/S0219498820501133 | MR 4120090
[17] Loday J.-L.: Cyclic Homology. Grundlehren der mathematischen Wissenschaften, 301, Springer, Berlin, 1992. MR 1217970
[18] Loday J.-L.: Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Enseign. Math. (2) 39 (1993), no. 3–4, 269–293 (French). MR 1252069 | Zbl 0806.55009
[19] Loday J.-L., Pirashvili T.: Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 296 (1993), no. 1, 139–158. DOI 10.1007/BF01445099 | MR 1213376 | Zbl 0821.17022
[20] Yashchuk V. S.: On some Leibniz algebras, having small dimension. Algebra Discrete Math. 27 (2019), no. 2, 292–308. MR 3982309
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