Quasi-definite axial algebras of Jordan type half

Abstract

Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents whose action on an
algebra is semisimple, and the fusion laws on the products between eigenvectors for these idempotents are fulfilled. We find the sufficient conditions in terms of the Frobenius form and of the properties of idempotents under which an axial algebra of Jordan type half is unital and has a finite capacity