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