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It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras and can be seen as a preliminary step to quantum Moufang loops. 1 Moufang loops It is well known how the Lie algebras are connected with the Lie groups. In the present paper, it is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. A Moufang loop [1, 2] is a quasigroup G with the identity element e ∈ G and the Moufang identity (ag)(ha) = a(gh)a, a, g, h ∈ G. Here the multiplication is denoted by juxtaposition. In general, the multiplication need not be associative: gh · a 6= g · ha. Inverse element g of g is defined by gg = gg = e. The left (L) and right (R) translations are defined by gh = Lgh = Rhg, g, h ∈ G. Both translations are inverible mappings and L g = Lg−1 , R −1 g = Rg−1 2 Analytic Moufang loops and infinitesimal Moufang translations Following the concept of the Lie group, the notion of an analytic Moufang loop can be easily formulated. Presented at the 12th Colloquium “Quantum Groups and Integrable Systems”, Prague, 12-14 June 2003 A Moufang loop G is said [3] to be analytic if G is also a real analytic manifold and main operations multiplication and the inversion map g 7→ g are analytic mappings. Let Te(G) denote the tangent space of G at the unit e. For x ∈ Te(G), infinitesimal Moufang translations are defined as vector fields on G as follows: Lx := Lx(g) := (dLg)ex ∈ Tg(G), Rx := Rx(g) := (dRg)ex ∈ Tg(G). Let the local coordinates of g from the vicinity of e ∈ G be denoted by g (i = 1, . . . , r := dimG). Define the auxiliary functions Lij(g) := ∂(gh) ∂hj ∣