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Automorphism groups of axial algebras

Gorshkov, Ilya
; 
McInroy, Justin
; 
Mudziiri Shumba, Tendai
; 
Shpectorov, Sergey
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Affiliation
Sobolev Institute of Mathematics; University of Chester; University of Bristol; University of Birmingham
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Publication Date
2024-08-22
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Mathematics
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Abstract
Axial algebras are a class of commutative non-associative algebras which have a natural group of automorphisms, called the Miyamoto group. The motivating example is the Griess algebra which has the Monster sporadic simple group as its Miyamoto group. Previously, using an expansion algorithm, about 200 examples of axial algebras in the same class as the Griess algebra have been constructed in dimensions up to about 300. In this list, we see many reoccurring dimensions which suggests that there may be some unexpected isomorphisms. Such isomorphisms can be found when the full automorphism groups of the algebras are known. Hence, in this paper, we develop methods for computing the full automorphism groups of axial algebras and apply them to a number of examples of dimensions up to 151.
Citation
Gorshkov, I., McInroy, J., Mudziiri Shumba, T., & Shpectorov, S. (2025). Automorphism groups of axial algebras. Journal of Algebra, 661, 657-712. https://doi.org/10.1016/j.jalgebra.2024.08.007
Publisher
Elsevier
Journal
Journal of Algebra
Research Unit
URI
http://hdl.handle.net/10034/628958
DOI
10.1016/j.jalgebra.2024.08.007
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Article
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ISSN
0021-8693
EISSN
1090-266X
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https://www.sciencedirect.com/science/article/pii/S0021869324004617