Geodesic
Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
Canadian journal of mathematics, Tome 60 (2008) no. 2, pp. 266-296

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

We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions. The bases for this algebra are indexed by set partitions. We show that there exists a natural inclusion of the Hopf algebra of noncommutative symmetric functions in this larger space. We also consider this algebra as a subspace of noncommutative polynomials and use it to understand the structure of the spaces of harmonics and coinvariants with respect to this collection of noncommutative polynomials and conclude two analogues of Chevalley’s theorem in the noncommutative setting.
DOI : 10.4153/CJM-2008-013-4
Mots-clés : 16W30, 05A18, 05E10 
Bergeron, Nantel; Reutenauer, Christophe; Rosas, Mercedes; Zabrocki, Mike. Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables. Canadian journal of mathematics, Tome 60 (2008) no. 2, pp. 266-296. doi: 10.4153/CJM-2008-013-4
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