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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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DOI

10.1016/0195-6701(84)90058-6

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1432-0916

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Multipermutation Solutions of the Yang–Baxter Equa

Authors: Tatiana GatevaIvanova Peter Cameron
Publish Date: 2011/12/13
Volume: 309, Issue: 3, Pages: 583-621
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Abstract

We examine solutions here mainly from the point of view of permutation groups a solution gives rise to a map from X to the symmetric group SymX on X satisfying certain conditions whose image we call a Yang–Baxter permutation group Our results include new constructions based on strong twisted unions with an investigation of retracts and the multipermutation level and the solvable length of the groups defined by the solutions new results about decompositions of solutions of arbitrary cardinality into invariant subsets and decompositions and factorisations of the associated Yang–Baxter group as a product of groups of the solutions defined by these invariant subsets In particular we obtain strong decomposition results if the Yang–Baxter permutation group is abelian or the solution is of finite multipermutation level

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  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
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  19. Continuity of the Lyapunov Exponents for Quasiperiodic Cocycles
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