Primitive axial algebras of Jordan type

  title={Primitive axial algebras of Jordan type},
  author={Jonathan I. Hall and Fabienne Rehren and Sergey V. Shpectorov},
Abstract An axial algebra over the field F is a commutative algebra generated by idempotents whose adjoint action has multiplicity-free minimal polynomial. For semisimple associative algebras this leads to sums of copies of F . Here we consider the first nonassociative case, where adjoint minimal polynomials divide ( x − 1 ) x ( x − η ) for fixed 0 ≠ η ≠ 1 . Jordan algebras arise when η = 1 2 , but our motivating examples are certain Griess algebras of vertex operator algebras and the related… CONTINUE READING

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