On the algebra of quasi-shuffles
| dc.creator | Loday, Jean-Louis | |
| dc.date | 2005-06-24 | |
| dc.date | 2007-02-15 | |
| dc.date.accessioned | 2026-07-07T08:07:01Z | |
| dc.date.available | 2026-07-07T08:07:01Z | |
| dc.description | For any commutative algebra $R$ the shuffle product on the tensor module $T(R)$ can be deformed to a new product. It is called the quasi-shuffle algebra, or stuffle algebra, and denoted $T^q(R)$. We show that if $R$ is the polynomial algebra, then $T^q(R)$ is free for some algebraic structure called Commutative TriDendriform (CTD-algebras). This result is part of a structure theorem for CTD-bialgebras which are associative as coalgebras and whose primitive part is commutative. In other words, there is a good triple of operads $(As, CTD, Com)$ analogous to $(Com, As, Lie)$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506498 | |
| dc.identifier | http://arxiv.org/abs/math/0506498 | |
| dc.identifier | Manuscripta Mathematica 123 (2007), no. 1, 79--93 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130801 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16A24; 16W30; 17A30; 18D50; 81R60 | |
| dc.title | On the algebra of quasi-shuffles | |
| dc.type | text |