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2019•Communications in AlgebraRequires access

Three-dimensional zeropotent algebras over an algebraically closed field of characteristic two

Kiyoshi Shirayanagi, Yuji Kobayashi, Sin‐Ei Takahasi, Makoto Tsukada

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Abstract

We 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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What this paper is about

We 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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Available abstract

We 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.

Key concepts: Algebraically closed field, Mathematics, Isomorphism (crystallography), Field (mathematics), Pure mathematics, Transformation (genetics), Algebra over a field, Crystal structure

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