The generalized definition equation of a G-weighted metric ds~2 from the datum of any group G acting onto a vector space mapped by a continuous numerical function μ, is applied when E = R~n and G = the group of translations in R~n. Here, G does not act linearly in R~n and R~n is considered as an affine space. The solution reads ds~2 = - d~2(ln I)/(Bp), I = (4iπx~0)~(n/2) · Ψ, where x~0 = -i/(2p), Ψ is a solution of the Schroedinger-type equation ΔΨ + i (partial deriv)Φ/(partial deriv)x~0 = 0, and B is a uniform term depending on x~0. When n = 3, p is interpreted as the reciprocal of a time variable. Attempts to identify ds~2 with the spatial part of a space-time metric of general relativity failed except for the flat Robertson and Walker spaces. In the simplest case, B = 1/R~2(t) and Ψ(p, r) = e~(-pr~2/2). A uniform but non-constant "imaginary potential energy" of the space can be formally derived: V(x~0) = 3i/(2x~0). Despite a striking formal link with tools of physical mathematics, no physical validation of the propositions of chemical algebra is claimed.
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