  
  
                                  [1X YangBaxter [101X
  
  
             [1X Combinatorial Solutions for the Yang-Baxter equation [101X
  
  
                                     0.10.7
  
  
                                  14 July 2025
  
  
                               Leandro Vendramin
  
                               Olexandr Konovalov
  
  
  
  Leandro Vendramin
      Email:    [7Xmailto:Leandro.Vendramin@vub.be[107X
      Homepage: [7Xhttps://vendramin.github.io/[107X
      Address:  [33X[0;14YVrije Universiteit Brussel[133X
                [33X[0;14YFaculty of Sciences[133X
                [33X[0;14YDepartment of Mathematics and Data Science[133X
                [33X[0;14YPleinlaan 2, B-1050[133X
                [33X[0;14YBrussel, Belgium[133X
  
  
  Olexandr Konovalov
      Email:    [7Xmailto:obk1@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://olexandr-konovalov.github.io/[107X
      Address:  [33X[0;14YSchool of Computer Science[133X
                [33X[0;14YUniversity of St Andrews[133X
                [33X[0;14YJack Cole Building, North Haugh,[133X
                [33X[0;14YSt Andrews, Fife, KY16 9SX, Scotland[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (YangBaxter)[101X
  
  1 [33X[0;0YPreliminaries[133X
    1.1 [33X[0;0YDefinition and examples[133X
      1.1-1 IsSkewbrace
      1.1-2 Skewbrace
      1.1-3 SmallSkewbrace
      1.1-4 TrivialBrace
      1.1-5 TrivialSkewbrace
      1.1-6 SmallBrace
      1.1-7 IdSkewbrace
      1.1-8 AutomorphismGroup
      1.1-9 IdBrace
      1.1-10 IsomorphismSkewbraces
      1.1-11 DirectProductSkewbraces
      1.1-12 DirectProductOp
      1.1-13 IsTwoSided
      1.1-14 IsAutomorphismGroupOfSkewbrace
      1.1-15 IsClassical
      1.1-16 IsOfAbelianType
      1.1-17 IsBiSkewbrace
      1.1-18 IsOfNilpotentType
      1.1-19 IsTrivialSkewbrace
      1.1-20 Skewbrace2YB
      1.1-21 Brace2YB
      1.1-22 SkewbraceSubset2YB
      1.1-23 SemidirectProduct
      1.1-24 UnderlyingAdditiveGroup
      1.1-25 UnderlyingMultiplicativeGroup
  2 [33X[0;0YAlgebraic Properties of Braces[133X
    2.1 [33X[0;0YBraces and Radical Rings[133X
      2.1-1 AdditiveGroupOfRing
      2.1-2 IsJacobsonRadical
    2.2 [33X[0;0YBraces and Yang-Baxter Equation[133X
      2.2-1 Table2YB
      2.2-2 Evaluate
      2.2-3 LyubashenkoYB
      2.2-4 IsIndecomposable
      2.2-5 Table
      2.2-6 DehornoyClass
      2.2-7 DehornoyRepresentationOfStructureGroup
      2.2-8 IdYB
      2.2-9 LinearRepresentationOfStructureGroup
  3 [33X[0;0YYangBaxter automatic generated documentation[133X
    3.1 [33X[0;0YYangBaxter automatic generated documentation of properties[133X
      3.1-1 IsIndecomposable
  4 [33X[0;0YIdeals and left ideals[133X
    4.1 [33X[0;0YLeft ideals[133X
      4.1-1 LeftIdeals
      4.1-2 StrongLeftIdeals
      4.1-3 IsLeftIdeal
    4.2 [33X[0;0YIdeals[133X
      4.2-1 IsIdeal
      4.2-2 Ideals
      4.2-3 AsIdeal
      4.2-4 IdealGeneratedBy
      4.2-5 IntersectionOfTwoIdeals
      4.2-6 SumOfTwoIdeals
    4.3 [33X[0;0YSequences (left) ideals[133X
      4.3-1 LeftSeries
      4.3-2 RightSeries
      4.3-3 IsLeftNilpotent
      4.3-4 IsSimpleSkewbrace
      4.3-5 IsRightNilpotent
      4.3-6 LeftNilpotentIdeals
      4.3-7 RightNilpotentIdeals
      4.3-8 SmoktunowiczSeries
      4.3-9 Socle
      4.3-10 Annihilator
    4.4 [33X[0;0YMutipermutation skew braces[133X
      4.4-1 SocleSeries
      4.4-2 MultipermutationLevel
      4.4-3 IsMultipermutation
      4.4-4 Fix
      4.4-5 KernelOfLambda
      4.4-6 Quotient
    4.5 [33X[0;0YPrime and semiprime ideals[133X
      4.5-1 IsPrimeBrace
      4.5-2 IsPrimeIdeal
      4.5-3 PrimeIdeals
      4.5-4 IsSemiprime
      4.5-5 IsSemiprimeIdeal
      4.5-6 SemiprimeIdeals
      4.5-7 BaerRadical
      4.5-8 IsBaer
      4.5-9 WedderburnRadical
      4.5-10 SolvableSeries
      4.5-11 IsMinimalIdeal
      4.5-12 MinimalIdeals
  
  
  [32X
