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Construct left non-degenerate cubic solutions to the Yang-Baxter equation

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Left non-degeneraete cubic solutions to the Yang-Baxter equation

Basic steps:

  • construct all shelves up to isomorphism such that the associated solution is cubic.
  • construct all solutions up to isomorphism with a given shelf as derived solution.

Count

  • all solutions obtained
  • all involutive solutions
  • all derived solutions

Construct YB semitrusses

Basic steps:

  • construct all dervied cubic YB semitrusses
  • for each derived cubic YB semitruss, construct all possible lambda-maps
  • for each possible lambda-map, construct, if exist, all possible circle operations.

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Construct left non-degenerate cubic solutions to the Yang-Baxter equation

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