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Corestricted group actions and eight-dimensional absolute valued algebras. (English) Zbl 1369.17003

Summary: We define and study the class of left reflection algebras, which is a subclass of eight-dimensional absolute valued algebras. We reduce its classification problem to the problem of finding a transversal for the action of a subgroup of \(O_7\) on \(O_7\) by conjugation. As a basis for this study, we give a general criterion for finding full subcategories of group action categories, which themselves arise from group actions.

MSC:

17A80 Valued algebras
17A35 Nonassociative division algebras
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
20B07 General theory for infinite permutation groups
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References:

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