The primitives of the Hopf algebra of noncommutative symmetric functions

Details The primitives of the Hopf algebra of noncommutative symmetric functions The primitives of the Hopf algebra of noncommutative symmetric functions

2004-10-16

arxiv.org/abs/math/0410365v1

Mathematics

Quantum Algebra

26 pages. The primitives are described over the integers (not over a characteristic zero field, which is much easier)

Scientific paper

Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it. This gives another proof of the theorem that the algebra of quasi-symmetric functions is free over the integers.

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