@article{Kongsomprach_Pongprasert_Rungratgasame_Tiansa-ard_2024, title={Completeness of Low-Dimensional Leibniz Algebras: Annual Meeting in Mathematics 2023}, volume={22}, url={https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1607}, abstractNote={<p>Leibniz algebras are generalizations of Lie algebras. By using the classification results of low-dimensional non-Lie nilpotent and non-nilpotent solvable Leibniz algebras obtained earlier, we define a basis of the derivation algebra Der(A) of each Leibniz algebra A and study their properties. It is known that for a Leibniz algebra A if the Lie algebra A / Leib(A) is complete, then A is a complete Leibniz algebra. We show that the converse holds when A is a complete solvable Leibniz algebra with dim(A) \leq 3. It is also known that for the derivation algebra of a complete Lie algebra is complete. However, our results show that this is not true for Leibniz algebras.</p>}, number={1}, journal={Thai Journal of Mathematics}, author={Kongsomprach, Yannawat and Pongprasert, Suchada and Rungratgasame, Thitarie and Tiansa-ard, Satrirat}, year={2024}, month={Mar.}, pages={165–178} }