Commutator
Groups, moves and rules · [u, v] = u·v·u⁻¹·v⁻¹
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A chain of four moves: do u, do v, undo u, undo v. If the moves u and v can be swapped (they are “friends”), the commutator equals “nothing was done”. In the game “step and lift” the second rule says that the commutator of the half-circle x³ and the hook t·x²·t⁻¹ equals one.
Read more: How many rules does a game need: a step and a lift
Where it appears · 1
- How many rules does a game need · Research