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According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility condition. Following their definition, we shall develop the theory of representations of skew braces. We show that the analogs of Maschke's theorem and Clifford's theorem hold for skew braces. We also study irreducible representations in prime characteristic.
Kozakai et al. (Tue,) studied this question.
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