Geodesic
On the Garsia Lie Idempotent
Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 445-454

Voir la notice de l'article provenant de la source Cambridge University Press

The orthogonal projection of the free associative algebra onto the free Lie algebra is afforded by an idempotent in the rational group algebra of the symmetric group ${{S}_{n}}$ , in each homogenous degree $n$ . We give various characterizations of this Lie idempotent and show that it is uniquely determined by a certain unit in the group algebra of ${{S}_{n-1}}$ . The inverse of this unit, or, equivalently, the Gram matrix of the orthogonal projection, is described explicitly. We also show that the Garsia Lie idempotent is not constant on descent classes (in fact, not even on coplactic classes) in ${{S}_{n}}$ .
DOI : 10.4153/CMB-2005-041-x
Mots-clés : 17B01, 05A99, 16S30, 17B60 
Patras, Frédéric; Reutenauer, Christophe; Schocker, Manfred. On the Garsia Lie Idempotent. Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 445-454. doi: 10.4153/CMB-2005-041-x
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