The description of the automorphism groups of finite-dimensional cyclic Leibniz algebras
DOI:
https://doi.org/10.15407/dopovidi2022.02.012Keywords:
Leibniz algebra, automorphism group, module over an associative ringAbstract
In the study of Leibniz algebras, the information about their automorphisms (as well as about endomorphisms, derivations, etc.) is very useful. We describe the automorphism groups of finite-dimensional cyclic Leibniz algebras. In particular, we consider the natural relationships between Leibniz algebras, groups and modules over associative rings.
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Blokh, A. (1965). A generalization of the concept of a Lie algebra. Dokl. Akad. Nauk SSSR, 165, No. 3, pp. 471-473 (in Russian).
Loday, J.-L. (1992). Cyclic homology. Grundlehren der mathematischen wissenschaften, Vol. 301. Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-662-21739-9
Loday, J.-L. (1993). Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Enseign. Math., 39, pp. 269-293. https://doi.org/10.5169/seals-60428
Loday, J.-L. & Pirashvili, T. (1993). Universal enveloping algebras of Leibniz algebras and (co)homology.
Math. Ann., 296, No. 1, pp. 139-158. https://doi.org/10.1007/BF01445099
Ayupov, S. A., Omirov, B. A. & Rakhimov, I. S. (2020). Leibniz algebras: structure and classification. Boca Raton: CRC Press, Taylor & Francis Group.
Kirichenko, V. V., Kurdachenko, L. A., Pypka, A. A. & Subbotin, I. Ya. (2017). Some aspects of Leibniz algebra theory. Algebra Discrete Math., 24, No. 1, pp. 1-33.
Chupordia, V. A., Pypka, A. A., Semko, N. N. & Yashchuk, V. S. (2019). Leibniz algebras: a brief review of current results. Carpathian Math. Publ., 11, No. 2, pp. 250-257. https://doi.org/0.15330/cmp.11.2.250-257
Kurdachenko, L. A., Semko, N. N. & Subbotin, I. Ya. (2020). Applying group theory philosophy to Leibniz algebras: some new developments. Adv. Group Theory Appl., 9, pp. 71-121. https://doi.org/10.32037/agta-2020-004
Ayupov, Sh., Kudaybergenov, K., Omirov, B. & Zhao, K. (2020). Semisimple Leibniz algebras, their derivations and automorphisms. Linear Multilinear Algebra, 68, No. 10, pp. 2005-2019. https://doi.org/10.1080/03081087.2019.1567674
Ladra, M., Rikhsiboev, I. M. & Turdibaev, R.M. (2016). Automorphisms and derivations of Leibniz algebras. Ukrainian Math. J., 68, No. 7, pp. 1062-1076. https://doi.org/10.1007/s11253-016-1277-3
Kurdachenko, L. A., Subbotin, I. Ya. & Yashchuk, V. S. (2021). On the endomorphisms and derivations of some Leibniz algebras. arXiv:2104.05922.
Chupordia, V. A., Kurdachenko, L. A. & Subbotin, I. Ya. (2017). On some ‘’minimal’’ Leibniz algebras.
J. Algebra Appl., 16, No. 5, 1750082. https://doi.org/10.1142/S0219498817500827
Kurdachenko, L. A., Otal, J. & Pypka, A. A. (2016). Relationships between factors of canonical central series of Leibniz algebras. Eur. J. Math., 2, pp. 565-577. https://doi.org/10.1007/s40879-016-0093-5
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