Title:
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On Leibniz algebras with maximal cyclic subalgebras (English) |
Author:
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Chupordia, Vasiliy A. |
Author:
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Kurdachenko, Leonid A. |
Author:
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Subbotin, Igor Ya. |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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63 |
Issue:
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3 |
Year:
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2022 |
Pages:
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277-294 |
Summary lang:
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English |
. |
Category:
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math |
. |
Summary:
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We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras. (English) |
Keyword:
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Leibniz algebra |
Keyword:
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Lie algebra |
Keyword:
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ideal |
Keyword:
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cyclic Leibniz algebra |
Keyword:
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derivation |
MSC:
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17A32 |
MSC:
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17A60 |
MSC:
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17A99 |
idZBL:
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Zbl 07655800 |
idMR:
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MR4542789 |
DOI:
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10.14712/1213-7243.2023.001 |
. |
Date available:
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2023-02-01T12:02:11Z |
Last updated:
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2024-10-04 |
Stable URL:
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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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