6 papers
-generated axial algebras with a minimal Miyamoto group
Justin McInroy
Axial algebras are a recently introduced class of non-associative algebra, with a naturally associated group, which generalise the Griess algebra and some key features of the moons…
Miyamoto groups of code algebras
Alonso Castillo-Ramirez, Justin McInroy
A code algebra is a nonassociative commutative algebra defined via a binary linear code . In a previous paper, we classified when code algebras are -graded a…
Enumerating 3-generated axial algebras of Monster type
Sanhan Khasraw, Justin McInroy, Sergey Shpectorov
An axial algebra is a commutative non-associative algebra generated by axes, that is, primitive, semisimple idempotents whose eigenvectors multiply according to a certain fusion la…
On the structure of axial algebras
Sanhan Khasraw, Justin McInroy, Sergey Shpectorov
Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial…
An expansion algorithm for constructing axial algebras
Justin McInroy, Sergey Shpectorov
An axial algebra is a commutative non-associative algebra generated by primitive idempotents, called axes, whose adjoint action on is semisimple and multiplication of eigen…
Code algebras which are axial algebras and their -gradings
Alonso Castillo-Ramirez, Justin McInroy
A code algebra is a non-associative commutative algebra defined via a binary linear code . We study certain idempotents in code algebras, which we call small idempotents,…