Remm E and Goze M
We classify, up to isomorphism, the 2-dimensional algebras over a field ï‹. We focuse also on the case of characteristic 2, identifying the matrices of GL(2, ï†2) with the elements of the symmetric group Σ3. The classification is then given by the study of the orbits of this group on a 3-dimensional plane, viewed as a Fano plane. As applications, we establish classifications of Jordan algebras, algebras of Lie type or Hom-Associative algebras.
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