Artículo
Invariants and coinvariants of the symmetric group in noncommuting variables
Autor/es | Bergeron, Nantel
Reutenauer, Christophe Rosas Celis, Mercedes Helena Zabrocki, Mike |
Departamento | Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2008 |
Fecha de depósito | 2016-07-04 |
Publicado en |
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Resumen | 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 ... 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. |
Cita | Bergeron, N., Reutenauer, C., Rosas Celis, M.H. y Zabrocki, M. (2008). Invariants and coinvariants of the symmetric group in noncommuting variables. Canadian Journal of Mathematics, 60 (2), 266-296. |
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