Study on Nilpotent Lie Group's Malcev Coordinate Transformation
Let G be a nilpotent Lie group of dimension m,g a Lie Algebra associated with G,and exp:g→G an exponential mapping.Let{X1,X2,⋯,Xm}be a set of bases of g,and according to the Campbell-Bak-m er-Hausdorff formula,we know exp(t1 X1)exp(t2 X2)⋯exp(tm Xm)=exp(m∑i=1Pi(t)Xi).We use the properties of the Malcev base coordinates to calculate the specific expression of the base transformation polynomial and indicate what kind of polynomial is the Malcev basis transformation polynomia.
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