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Graded 2-generated axial algebras

2020/05/07 by Whybrow, Madeleine
#17D99 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2005.03577

Abstract

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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