Affine Connections and Loopuscular Structures

Abstract

A. Tangent affine connections of loopuscular structures 8.1. Recall that a partial left loopuscular algebra M = 〈M, L〉 is said to be left (p, k)-canonical if, for any a ∈ M, its left loop M.a = 〈M,, a〉, where xy = L(x,a, y),has, near a, C^p-smooth (p≥1) left fundamental vector fields 131-1 defined by see Definitions 3.27, 3.31. Instead of ‘left (1, k)-canonical’ we usually say ‘left canonical’.