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The Algebra of Quasi-Symmetric Functions Is Free over the Integers

✍ Scribed by Michiel Hazewinkel

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 144 KB
Volume: 164
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2001.2017

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✦ Synopsis

Let Z denote the Leibniz-Hopf algebra, which also turns up as the Solomon descent algebra and the algebra of noncommutative symmetric functions. As an algebra Z=ZOZ 1 , Z 2 , ...P, the free associative algebra over the integers in countably many indeterminates. The coalgebra structure is given by m(Z n )=; n i=0 Z i é Z n -i , Z 0 =1. Let M be the graded dual of Z. This is the algebra of quasi-symmetric functions. The Ditters conjecture says that this algebra is a free commutative algebra over the integers. In this paper the Ditters conjecture is proved.

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