Axial Algebras: Questions and Conjectures

Abstract

Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead to automorphisms of the algebra, and so such axial algebras are inextricably linked with groups. This article is meant to complement the recent survey \cite{ms} by significantly expanding the list of interesting open problems suggested by the specialists in the field, and providing a further discussion of the related concepts and available results.