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From forbidden configurations to a classification of some axial algebras of Monster type
McInroy, Justin Shpectorov, Sergey
McInroy, Justin
Shpectorov, Sergey
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2023-03-17
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Abstract
Ivanov introduced the shape of a Majorana algebra as a record of the 2-generated subalgebras arising in that algebra. As a broad generalisation of this concept and to free it from the ambient algebra, we introduce the concept of an axet and shapes on an axet. A shape can be viewed as an algebra version of a group amalgam. Just like an amalgam, a shape leads to a unique algebra completion which may be non-trivial or it may collapse. Then for a natural family of shapes of generalised Monster type we classify all completion algebras and discover that a great majority of them collapse, confirming the observations made in an earlier paper [12].
Citation
McInroy, J., & Shpectorov, S. (2023). From forbidden configurations to a classification of some axial algebras of Monster type. Journal of Algebra, 627, 58-105. https://doi.org/10.1016/j.jalgebra.2023.03.003
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Elsevier
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Journal of Algebra
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Article
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0021-8693
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1090-266X