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Generating sets of F/R' Leibniz algebras

  • Zeynep Özkurt ORCID logo EMAIL logo
Published/Copyright: July 25, 2023
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Abstract

Let F be a free Leibniz algebra generated by the set X = { x 1 , , x n } over the field K of characteristic 0 and let R be an ideal of F. In this study, a necessary and sufficient condition for n elements of the Leibniz algebra F / R to be a generating set is given.

MSC 2020: 17A32; 17A36

Acknowledgements

The author is very grateful to the anonymous referee for the careful reading of the manuscript and the valuable suggestions for the improvement of the exposition.

References

[1] Y. Bahturin and S. Nabiyev, Automorphisms and derivations of abelian extensions of some Lie algebras, Abh. Math. Semin. Univ. Hamburg 62 (1992), 43–57. 10.1007/BF02941617Search in Google Scholar

[2] J. S. Birman, An inverse function theorem for free groups, Proc. Amer. Math. Soc. 41 (1973), 634–638. 10.1090/S0002-9939-1973-0330295-8Search in Google Scholar

[3] J.-L. Loday and T. Pirashvili, Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Ann. 296 (1993), no. 1, 139–158. 10.1007/BF01445099Search in Google Scholar

[4] A. A. Mikhalev and U. U. Umirbaev, Subalgebras of free Leibniz algebras, Comm. Algebra 26 (1998), no. 2, 435–446. 10.1080/00927879808826139Search in Google Scholar

[5] V. Shpilrain, On generators of L / R 2 Lie algebras, Proc. Amer. Math. Soc. 119 (1993), no. 4, 1039–1043. 10.1090/S0002-9939-1993-1154249-XSearch in Google Scholar

[6] A. L. Šmelkin, Wreath products of Lie algebras, and their application in group theory (in Russian), Trudy Moskov. Mat. Obšč. 29 (1973), 247–260. Search in Google Scholar

[7] T. Taş Adıyaman and Z. Özkurt, Automorphisms of free metabelian Leibniz algebras of rank three, Turkish J. Math. 43 (2019), no. 5, 2262–2274. 10.3906/mat-1903-104Search in Google Scholar

[8] T. Taş Adiyaman and Z. Özkurt, Automorphisms of free metabelian Leibniz algebras, Comm. Algebra 49 (2021), no. 10, 4348–4359. 10.1080/00927872.2021.1919690Search in Google Scholar

[9] U. U. Umirbaev, Partial derivations and endomorphisms of some relatively free Lie algebras (in Russian), Sibirsk. Mat. Zh. 34 (1993), no. 6, 179–188; translation in Siberian Math. J. 34 (1993), no. 6, 1161–1170. Search in Google Scholar

Received: 2022-07-07
Revised: 2023-02-02
Accepted: 2023-05-23
Published Online: 2023-07-25
Published in Print: 2023-10-01

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