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Graded 2-generated axial algebras

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arxiv 2005.03577 v1 pith:YGB7Y3ZJ submitted 2020-05-07 math.RA math.GR

Madeleine Whybrow This is my paper · ORCID
classification math.RAmath.GR
keywords algebrasaxialgeneratedfusionwhoseeigenvaluesgradedidempotents
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Axial algebras are non-associative algebras generated by semisimple idempotents whose adjoint actions obey a fusion law. Axial algebras that are generated by two such idempotents play a crucial role in the theory. We classify all primitive 2-generated axial algebras whose fusion laws have two eigenvalues and all graded primitive 2-generated axial algebras whose fusion laws have three eigenvalues. This represents a significant broadening in our understanding of axial algebras.

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