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Title: On Leibniz algebras with maximal cyclic subalgebras (English)
Author: Chupordia, Vasiliy A.
Author: Kurdachenko, Leonid A.
Author: Subbotin, Igor Ya.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 63
Issue: 3
Year: 2022
Pages: 277-294
Summary lang: English
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Category: math
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Summary: We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras. (English)
Keyword: Leibniz algebra
Keyword: Lie algebra
Keyword: ideal
Keyword: cyclic Leibniz algebra
Keyword: derivation
MSC: 17A32
MSC: 17A60
MSC: 17A99
idZBL: Zbl 07655800
idMR: MR4542789
DOI: 10.14712/1213-7243.2023.001
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Date available: 2023-02-01T12:02:11Z
Last updated: 2023-04-20
Stable URL: http://hdl.handle.net/10338.dmlcz/151476
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Reference: [1] Ayupov Sh., Omirov B., Rakhimov I.: Leibniz Algebras: Structure and Classification.CRC Press, Boca Raton, 2020.
Reference: [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. MR 3169714, 10.1080/00927872.2012.717655
Reference: [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
Reference: [4] Bloh A. M.: On a generalization of the concept of Lie algebra.Dokl. Akad. Nauk SSSR 165 (1965), 471–473 (Russian). MR 0193114
Reference: [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. MR 4169625, 10.15407/dopovidi2020.07.017
Reference: [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. MR 3634087, 10.1142/S0219498817500827
Reference: [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
Reference: [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. MR 3499000, 10.1007/s40879-016-0093-5
Reference: [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
Reference: [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. MR 3613335, 10.1515/math-2017-0010
Reference: [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
Reference: [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
Reference: [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
Reference: [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
Reference: [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
Reference: [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. MR 4120090, 10.1142/S0219498820501133
Reference: [17] Loday J.-L.: Cyclic Homology.Grundlehren der mathematischen Wissenschaften, 301, Springer, Berlin, 1992. MR 1217970
Reference: [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). Zbl 0806.55009, MR 1252069
Reference: [19] Loday J.-L., Pirashvili T.: Universal enveloping algebras of Leibniz algebras and (co)homology.Math. Ann. 296 (1993), no. 1, 139–158. Zbl 0821.17022, MR 1213376, 10.1007/BF01445099
Reference: [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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