Three-dimensional zeropotent algebras over an algebraically closed field of characteristic two |
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| Authors: | Kiyoshi Shirayanagi Yuji Kobayashi Sin-Ei Takahasi Makoto Tsukada |
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| Affiliation: | 1. Department of Information Science, Toho University, Funabashi, Japan;2. kiyoshi.shirayanagi@is.sci.toho-u.ac.jp;4. Laboratory of Mathematics and Games, Funabashi, Japan |
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| Abstract: | AbstractWe previously classified three-dimensional zeropotent algebras over an algebraically closed field of any characteristic except for two. The exceptional case of characteristic two is special because some of the previous transformation matrices to verify isomorphism are unavailable. In this paper, we give new transformation matrices peculiar to characteristic two and then achieve classification in the exceptional case. We thus accomplish a classification of three-dimensional zeropotent algebras over an algebraically closed field of any characteristic. |
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| Keywords: | Nonassociative algebras anticommutative algebras zeropotent algebras lie algebras characteristic two |
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