8 papers · 1 filter
Axial algebras of Jordan and Monster type
Justin McInroy, Sergey Shpectorov
Axial algebras are a class of non-associative commutative algebras whose properties are defined in terms of a fusion law. When this fusion law is graded, the algebra has a naturall…
Quotients of the Highwater algebra and its cover
Clara Franchi, Mario Mainardis, Justin McInroy
Axial algebras are a class of non-associative algebra with a strong link to finite (especially simple) groups which have recently received much attention. Of primary interest are t…
Split spin factor algebras
J. McInroy, S. Shpectorov
Motivated by Yabe's classification of symmetric -generated axial algebras of Monster type, we introduce a large class of algebras of Monster type , generalisin…
-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…
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…