Classification of three-dimensional zeropotent algebras over an algebraically closed field |
| |
Authors: | Yuji Kobayashi Sin-Ei Takahasi Makoto Tsukada |
| |
Institution: | 1. Department of Information Science, Toho University, Funabashi, Chiba, Japan;2. Laboratory of Mathematics and Games, Funabashi, Chiba, Japan |
| |
Abstract: | A nonassociative algebra is defined to be zeropotent if the square of any element is zero. Zeropotent algebras are exactly the same as anticommutative algebras when the characteristic of the ground field is not two. The class of zeropotent algebras properly contains that of Lie algebras. In this paper, we give a complete classification of three-dimensional zeropotent algebras over an algebraically closed field of characteristic not equal to two. By restricting the result to the subclass of Lie algebras, we can obtain a classification of three-dimensional complex Lie algebras, which is in accordance with the conventional one. |
| |
Keywords: | Anticommutative algebras Jacobi element Lie algebras nonassociative algebras zeropotent algebras |
|
|