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Artículo
Grothendieck bialgebras, Partition lattices, and symmetric functions in noncommutative variables
(American Mathematical Society, 2006)
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism ...
Artículo
Invariants and coinvariants of the symmetric group in noncommuting variables
(University of Toronto Press, 2008)
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 ...