Lectures on deformations of complex manifolds

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Lie description of higher obstructions to deforming submanifolds (2005, background): “…natural extension of the differential d and the bracket [ , ] deﬁned as Since K 0 ⊗ m is a nilpotent Lie algebra, its exponential group exp ( K 0 ⊗ m ) can be deﬁned as the set { e a | a ∈ K 0 ⊗ m } ; we have e a e b = e a • b , where • is the Baker-Campbell-Hausdorff product (see e.g. [19,28]).”