The homotopy Lie algebra and the holonomy representation
In this section the ground ring is an arbitrary field k of characteristic zero. Recall from §21(d) that the homotopy Lie algebra, L x- of a simply connected topological space X is the graded vector space, equipped with a Lie bracket defined via the Whitehead product in π*(X). In particular, (cf. Example 2, §21) each x ∈ L x determines the linear transformation adx :L x → L x, given by
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