Abstract
Abstract Skew-braces are ring-like objects arising in connection with HopfâGalois theory and set-theoretic solutions đ to the YangâBaxter equation. Interactions between skew-braces are often related to đ-braces. For example, every đ-brace đŽ is given by a pair of skew-braces which induces a â€-indexed sequence of skew-braces. The sequence collapses if đŽ itself is a skew-brace. The free group over the underlying set of a solution đ is a đ-brace. Bi-crossed products of skew-braces are shown to be đ-braces, and criteria are developed when they are skew-braces. Two classes of skew-braces are put into a bijective correspondence with special đ-braces, which themselves need not be skew-braces. Characterizations of đ-braces, including one in terms of a graph and one as special modules over skew-braces, are given.
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