A characterization of the full wreath product

Hall, J. I.

doi:10.1016/j.jalgebra.2005.12.027

Journal of Algebra

2006

DOI: 10.1016/j.jalgebra.2005.12.027

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A characterization of the full wreath product

J. I. Hall

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Cited by 2 publications

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Modules over Axial Algebras

Medts

Couwenberghe

2018

Algebr Represent Theor

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We introduce axial representations and modules over axial algebras as new tools to study axial algebras. All known interesting examples of axial algebras fall into this setting, in particular the Griess algebra whose automorphism group is the Monster group. Our results become especially interesting for Matsuo algebras. We vitalize the connection between Matsuo algebras and 3-transposition groups by relating modules over Matsuo algebras with representations of 3-transposition groups. As a by-product, we define, given a Fischer space, a group that can fulfill the role of a universal 3-transposition group.

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Modules over Axial Algebras

Medts

Couwenberghe

2018

Algebr Represent Theor

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Moufang Loops and Groups with Triality are Essentially the Same Thing

Hall¹

2019

Memoirs of the AMS

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In 1925 Élie Cartan introduced the principal of triality specifically for the Lie groups of type D 4 D_4 , and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title was made by Stephen Doro in 1978 who was in turn motivated by work of George Glauberman from 1968. Here we make the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word “essentially.”

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A characterization of the full wreath product

Cited by 2 publications

References 23 publications

Modules over Axial Algebras

Modules over Axial Algebras

Moufang Loops and Groups with Triality are Essentially the Same Thing

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