Abstract Axial algebras are non-associative algebras generated by semisimple idempotents, called axes, that obey a fixed fusion law. Important examples of axial algebras include the Griess algebra and Jordan algebras. Axial algebras that are generated by two axes are called dihedral and are fundamental in the study of these algebras in general. We present an algorithm to classify and construct dihedral axial algebras. This work represents a significant broadening in our understanding of axial algebras.
Speaker: Madeleine Whybrow, Univerza na Primorskem
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