Lie algebra of a formal group law

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Definition

Suppose F is a n-dimensional formal group law over a commutative unital ring R. The Lie algebra of F is defined as the following Lie algebra L:

  • Additively, it is a free module R^n.
  • For any two elements x = (x_1,x_2,\dots,x_n) and y = (y_1,y_2,\dots,y_n), we define [x,y] as:

\! [x,y] := F_2(x,y) - F_2(y,x)

where F_2 is the degree two part of the expression for F.