  
  
                                  [1X YangBaxter [101X
  
  
             [1X Combinatorial Solutions for the Yang-Baxter equation [101X
  
  
                                     0.7.0
  
  
                                23 February 2019
  
  
                               Leandro Vendramin
  
                              Alexander Konovalov
  
  
  
  Leandro Vendramin
      Email:    [7Xmailto:lvendramin@dm.uba.ar[107X
      Homepage: [7Xhttp://mate.dm.uba.ar/~lvendram[107X
      Address:  [33X[0;14YDepartamento de matem'atica, FCEN, UBA[133X
                [33X[0;14YCiudad Universitaria, Pab. 1[133X
                [33X[0;14YBuenos Aires, Argentina[133X
  
  
  Alexander Konovalov
      Email:    [7Xmailto:alexander.konovalov@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://alexk.host.cs.st-andrews.ac.uk/[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
  
  
  
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  [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 IdBrace
      1.1-9 IsomorphismSkewbraces
      1.1-10 DirectProductSkewbraces
      1.1-11 IsTwoSided
      1.1-12 IsClassical
      1.1-13 IsTrivialSkewbrace
      1.1-14 Skewbrace2YB
      1.1-15 Brace2YB
      1.1-16 SkewbraceSubset2YB
  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 Evaluate
      2.2-2 LyubashenkoYB
      2.2-3 DehornoyClass
      2.2-4 LinearRepresentationOfStructureGroup
  3 [33X[0;0YIdeals and left ideals[133X
    3.1 [33X[0;0YLeft ideals[133X
      3.1-1 LeftIdeals
      3.1-2 IsLeftIdeal
    3.2 [33X[0;0YIdeals[133X
      3.2-1 IsIdeal
      3.2-2 Ideals
      3.2-3 AsIdeal
      3.2-4 IdealGeneratedBy
      3.2-5 IntersectionOfTwoIdeals
      3.2-6 SumOfTwoIdeals
    3.3 [33X[0;0YSequences (left) ideals[133X
      3.3-1 LeftSeries
      3.3-2 RightSeries
      3.3-3 IsLeftNilpotent
      3.3-4 IsSimpleSkewbrace
      3.3-5 IsRightNilpotent
      3.3-6 LeftNilpotentIdeals
      3.3-7 RightNilpotentIdeals
      3.3-8 SmoktunowiczSeries
      3.3-9 Socle
    3.4 [33X[0;0YMutipermutation skew braces[133X
      3.4-1 SocleSeries
      3.4-2 MultipermutationLevel
      3.4-3 IsMultipermutation
      3.4-4 Fix
      3.4-5 KernelOfLambda
      3.4-6 Quotient
    3.5 [33X[0;0YPrime and semiprime ideals[133X
      3.5-1 IsPrimeBrace
      3.5-2 IsPrimeIdeal
      3.5-3 PrimeIdeals
      3.5-4 IsSemiprime
      3.5-5 IsSemiprimeIdeal
      3.5-6 SemiprimeIdeals
      3.5-7 BaerRadical
      3.5-8 IsBaer
      3.5-9 WedderburnRadical
      3.5-10 SolvableSeries
      3.5-11 IsMinimalIdeal
      3.5-12 MinimalIdeals
  
  
  [32X
