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Register a new userOn the classification of 2-generated axial algebras of Majorana type
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Authors
Takahiro Yabe
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A class of axial algebras generated by two axes with eigenvalues 0, 1, $eta$ and $xi$ called axial algebras of Majorana type is introduced and classified when they are 2-generated, over fields of characteristics neither 2 nor 5 and there exists an automorphism switching generating axes.. The class includes deformations of nine Norton-Sakuma algebras. Over fields of characteristics 5, the axial algebras of Majorana type with the axial dimension at most 5 are clasified.
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A class of axial decomposition algebras with Miyamoto group generated by two Miyamoto automorphisms and three eigenvalues $0,1$ and $eta$ is introduced and classified in the case with $eta otin{0,1,frac{1}{2}}$. This class includes specializations of 2-generated axial algebras of Majorana type $(xi,eta)$ to the case with $xi=eta$.
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