The Algebra of Quasi-Symmetric Functions Is Free over the Integers
Author: Hazewinkel M.
Source: Advances in Mathematics, Volume 164, Number 2, December 2001 , pp. 283-300(18)
Publisher: Academic Press
Let denote the LeibnizHopf algebra, which also turns up as the Solomon descent algebra and the algebra of noncommutative symmetric functions. As an algebra =ZZ1, Z2, , the free associative algebra over the integers in countably many indeterminates. The coalgebra structure is given by (Zn)=ni=0 ZiZn-i, Z0=1. Let be the graded dual of . 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. © 2001 Elsevier Science.
Keywords: Leibniz; Hopf algebra; quasi-symmetric functions; Ditters conjecture; Lie; Hopf algebra; Solomon descent algebra; shuffle algebra; overlapping shuffle algebra; noncommutative symmetric functions; divided power sequences; coalgebra; Hopf algebra; free coalgebra; formal group; Lyndon words; symmetric group; symmetric functions; Hecke algebra
Document Type: Research article
Affiliations: CWI, Amsterdam, The Netherlands
Publication date: 2001-12-01