Enumerating 3-generated axial algebras of Monster type

Justin McInroy; Sergey Shpectorov; Sanhan Khasraw

Enumerating 3-generated axial algebras of Monster type

Justin McInroy, Sergey Shpectorov, Sanhan Khasraw

Research output: Contribution to journal › Article (Academic Journal)

Abstract

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 law. The Griess algebra, whose automorphism group is the Monster, is an example of an axial algebra. We say an axial algebra is of Monster type if it has the same fusion law as the Griess algebra.
The 2-generated axial algebras of Monster type, called Norton-Sakuma algebras, have been fully classified and are one of nine isomorphism types. In this paper, we enumerate and construct the 3-generated axial algebras of Monster type which do not contain a 5A, or 6A subalgebra.

Original language	English
Number of pages	26
Journal	arXiv
Publication status	Published - 27 Sep 2018

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https://arxiv.org/pdf/1809.10657.pdf

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title = "Enumerating 3-generated axial algebras of Monster type",

abstract = "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 law. The Griess algebra, whose automorphism group is the Monster, is an example of an axial algebra. We say an axial algebra is of Monster type if it has the same fusion law as the Griess algebra. The 2-generated axial algebras of Monster type, called Norton-Sakuma algebras, have been fully classified and are one of nine isomorphism types. In this paper, we enumerate and construct the 3-generated axial algebras of Monster type which do not contain a 5A, or 6A subalgebra.",

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N2 - 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 law. The Griess algebra, whose automorphism group is the Monster, is an example of an axial algebra. We say an axial algebra is of Monster type if it has the same fusion law as the Griess algebra. The 2-generated axial algebras of Monster type, called Norton-Sakuma algebras, have been fully classified and are one of nine isomorphism types. In this paper, we enumerate and construct the 3-generated axial algebras of Monster type which do not contain a 5A, or 6A subalgebra.

AB - 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 law. The Griess algebra, whose automorphism group is the Monster, is an example of an axial algebra. We say an axial algebra is of Monster type if it has the same fusion law as the Griess algebra. The 2-generated axial algebras of Monster type, called Norton-Sakuma algebras, have been fully classified and are one of nine isomorphism types. In this paper, we enumerate and construct the 3-generated axial algebras of Monster type which do not contain a 5A, or 6A subalgebra.

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