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On axial algebras with $3$ eigenvalues
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math.RA
keywords
algebrasgeneratedactionsadjointaxialeigenvaluesfusioncase
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abstract
We study axial algebras, that is, commutative non-associative algebras generated by idempotents whose adjoint actions are semisimple and obey a fusion law. Considering the case, when said adjoint actions having $3$ eigenvalues and the fusion law is the least restrictive, we describe $2$-generated and $3$-generated algebras and prove some of their general properties.
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