Persistence of cyclic left distributive algebras Original Research Article

Let Ak = Ak(*) denote the left distributive groupoid on {0, 1, …, 2k − 1} such that a * 1 triple bond; length as m-dash a + 1 mod 2k for every a ε Ak. Let d ≥ 0 and put r = max {i; 2i divides d}. For a = ∑ ai2i ε Ak, ai ε {0, 1}, put νd(a) = ∑ aiνd(2i) and vd(2i) = 2(i + 1) 2d − 2i2d. Then vd: Ak → Ak2d is a groupoid homomorphism iff k ≤ 22r + 1.