Miyamoto groups of code algebras

Alonso Castillo-Ramirez; Justin McInroy

doi:10.1016/j.jpaa.2020.106619

Miyamoto groups of code algebras

Alonso Castillo-Ramirez, Justin McInroy

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Abstract

A code algebra $A_C$ is a nonassociative commutative algebra defined via a binary linear code $C$. In a previous paper, we classified when code algebras are $\mathbb{Z}_2$-graded axial algebras generated by small idempotents. In this paper, for each algebra in our classification, we obtain the Miyamoto group associated to the grading. We also show that the code algebra structure can be recovered from the axial algebra structure.

Original language	English
Article number	106619
Number of pages	19
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	6
Early online date	10 Nov 2020
DOIs	https://doi.org/10.1016/j.jpaa.2020.106619
Publication status	E-pub ahead of print - 10 Nov 2020

Keywords

math.GR
20B25, 17A99, 17D99, 94B05, 17B69

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10.1016/j.jpaa.2020.106619

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://doi.org/10.1016/j.jpaa.2020.106619. Please refer to any applicable terms of use of the publisher.
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abstract = " A code algebra $A_C$ is a nonassociative commutative algebra defined via a binary linear code $C$. In a previous paper, we classified when code algebras are $\mathbb{Z}_2$-graded axial algebras generated by small idempotents. In this paper, for each algebra in our classification, we obtain the Miyamoto group associated to the grading. We also show that the code algebra structure can be recovered from the axial algebra structure. ",

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AU - McInroy, Justin

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AB - A code algebra $A_C$ is a nonassociative commutative algebra defined via a binary linear code $C$. In a previous paper, we classified when code algebras are $\mathbb{Z}_2$-graded axial algebras generated by small idempotents. In this paper, for each algebra in our classification, we obtain the Miyamoto group associated to the grading. We also show that the code algebra structure can be recovered from the axial algebra structure.

KW - math.GR

KW - 20B25, 17A99, 17D99, 94B05, 17B69

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Miyamoto groups of code algebras

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