Skip to Main content Skip to Navigation
Conference papers

Combinatorial Hopf Algebras and Towers of Algebras

Abstract : Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n \geq 0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of algebras. We show that if a tower $\bigoplus_{n \geq 0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim (A_n)=r^nn!$ where $r = \dim (A_1)$.
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Wednesday, August 19, 2015 - 11:43:33 AM
Last modification on : Tuesday, October 6, 2020 - 10:56:02 AM
Long-term archiving on: : Friday, November 20, 2015 - 10:34:54 AM


Publisher files allowed on an open archive




Nantel Bergeron, Thomas Lam, Huilan Li. Combinatorial Hopf Algebras and Towers of Algebras. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.53-60, ⟨10.46298/dmtcs.3634⟩. ⟨hal-01185169⟩



Record views


Files downloads