Properties
The Whitehead product is bilinear, graded-symmetric, and satisfies the graded Jacobi identity, and is thus a graded quasi-Lie algebra; this is proven in Uehara & Massey (1957) via the Massey triple product.
If, then the Whitehead bracket is related to the usual conjugation action of on by
where denotes the conjugation of by . For, this reduces to
which is the usual commutator.
The relevant MSC code is: 55Q15, Whitehead products and generalizations.
Read more about this topic: Whitehead Product
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