Corestricted group actions and eight-dimensional absolute valued algebras

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 O7O7 on O7O7 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.