TY - JOUR
AU - Kongsomprach, Yannawat
AU - Pongprasert, Suchada
AU - Rungratgasame, Thitarie
AU - Tiansa-ard, Satrirat
PY - 2024/03/31
Y2 - 2024/06/18
TI - Completeness of Low-Dimensional Leibniz Algebras: Annual Meeting in Mathematics 2023
JF - Thai Journal of Mathematics
JA - Thai J Math
VL - 22
IS - 1
SE - Articles
DO -
UR - https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1607
SP - 165–178
AB - <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>
ER -