Every finite perfect two-sided skew brace decomposes as a central product of an almost trivial skew brace and a trivial skew brace, both arising from perfect groups, with perfectness equivalent for the brace and either underlying group.
Rump, Braces, radical rings, and the quantum Yang-Baxte r equation, J
3 Pith papers cite this work. Polarity classification is still indexing.
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Classification and structural description of simple involutive latin solutions to the Yang-Baxter equation with regular displacement group and nilpotent permutation group, including enumeration for size p^p.
Proves irreducibility of monomial representations equivalent to indecomposability of set-theoretic YBE solutions (except Dehornoy class two) and shows induction from one-dimensional representations.
citing papers explorer
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On finite perfect two-sided skew braces
Every finite perfect two-sided skew brace decomposes as a central product of an almost trivial skew brace and a trivial skew brace, both arising from perfect groups, with perfectness equivalent for the brace and either underlying group.
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Involutive (simple) latin solutions of the Yang-Baxter equation and related (left) quasigroups
Classification and structural description of simple involutive latin solutions to the Yang-Baxter equation with regular displacement group and nilpotent permutation group, including enumeration for size p^p.
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On Dehornoy's representation for the Yang-Baxter equation
Proves irreducibility of monomial representations equivalent to indecomposability of set-theoretic YBE solutions (except Dehornoy class two) and shows induction from one-dimensional representations.