NSym into Q_{\infty} is not a Hopf Map

Details NSym into Q_{\infty} is not a Hopf Map NSym into Q_{\infty} is not a Hopf Map

2004-10-28

arxiv.org/abs/math/0410591v2

Mathematics

Rings and Algebras

references added, some revisions

Scientific paper

There is a natural algebra map (in fact, embedding) from the noncommutative
symmetric functions NSym to the quadratic algebra Q_{\infty} of pseudoroots of
polynomials. In this note, I show that it is not a coalgebra map. Hence, the
Hopf algebra structure on NSym can't be extended to this important larger
algebra.

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