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arXiv · 2001.08426

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 (decomposition) 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 decomposition algebra structure.

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Alonso Castillo-Ramirez, Justin McInroy. 2020-01-23. Miyamoto groups of code algebras. https://doi.org/10.1016/j.jpaa.2020.106619

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