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YangBaxter

Combinatorial Solutions for the Yang-Baxter equation

0.10.6

17 July 2024

Leandro Vendramin
Email: Leandro.Vendramin@vub.be
Homepage: https://vendramin.github.io/
Address:
Vrije Universiteit Brussel
Faculty of Sciences
Department of Mathematics and Data Science
Pleinlaan 2, B-1050
Brussel, Belgium

Olexandr Konovalov
Email: obk1@st-andrews.ac.uk
Homepage: https://olexandr-konovalov.github.io/
Address:
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland

Contents

2 Algebraic Properties of Braces

2.1 Braces and Radical Rings

2.1-1 AdditiveGroupOfRing
2.1-2 IsJacobsonRadical

2.2 Braces and Yang-Baxter Equation

  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 YangBaxter automatic generated documentation

3.1 YangBaxter automatic generated documentation of properties

3.1-1 IsIndecomposable

4 Ideals and left ideals

4.1 Left ideals

  4.1-1 LeftIdeals
  4.1-2 StrongLeftIdeals
  4.1-3 IsLeftIdeal

  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 Sequences (left) ideals

  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 Mutipermutation skew braces

  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 Prime and semiprime ideals

  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

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