Torsors and Ternary Moufang Loops Arising in Projective Geometry
Torsors and Ternary Moufang Loops Arising in Projective Geometry
A projective space gives rise to an affine space $$V_a$$ by taking out a hyperplane $$a$$ . We define a natural ternary product on the set $$U_{ab} = V_a \cap V_b$$ , for any pair $$(a,b)$$ of hyperplanes. If the space is Desarguesian, we show that this ternary product is …