Abstract
This paper concerns the study of Leibniz algebras, a natural generalization of Lie algebras, from the perspective of centralizers of elements. We study conditions on Leibniz algebras under which centralizers of all elements are ideals. We call a Leibniz algebra, a CL-algebra if centralizers of all elements are ideals. We discuss nilpotency of CL-algebras.
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Acknowledgement
The second author would like to thank Prof. Ayupov of Institute of Mathematics, Uzbekistan Academy of Sciences and Prof. Karimbergen of Karakalpak State University, Uzbekistan for valuable discussions on this problem in a CIMPA research school on “Non-associative algebra and applications” held at Tashkent, Uzbekistan. The second author is especially thankful to Dr. Abror Kh. Khudoyberdiyev for reading a draft version of the article and his useful suggestions. The second author expresses his gratitude to CIMPA, France for their financial help to attend the research school. The Authors would like to thank the esteemed referee for her/his useful comments on the earlier version of the manuscript that have improved the exposition.
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Das, P., Saha, R. On Leibniz Algebras Whose Centralizers Are Ideals. Indian J Pure Appl Math 51, 1555–1571 (2020). https://doi.org/10.1007/s13226-020-0481-x
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DOI: https://doi.org/10.1007/s13226-020-0481-x