Combinatorial Hopf Algebras and Towers of Algebras
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...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3634/pdf |
| _version_ | 1797270428188672000 |
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| author | Nantel Bergeron Thomas Lam Huilan Li |
| author_facet | Nantel Bergeron Thomas Lam Huilan Li |
| author_sort | Nantel Bergeron |
| collection | DOAJ |
| description | 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 $r = \dim (A_1)$. |
| first_indexed | 2024-04-25T02:04:06Z |
| format | Article |
| id | doaj.art-85686023ad77426c9daea71fad7b5248 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:04:06Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-85686023ad77426c9daea71fad7b52482024-03-07T14:38:06ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01DMTCS Proceedings vol. AJ,...Proceedings10.46298/dmtcs.36343634Combinatorial Hopf Algebras and Towers of AlgebrasNantel Bergeron0https://orcid.org/0000-0002-4482-7427Thomas Lam1Huilan Li2Department of Mathematics and Statistics [Toronto]Department of Mathematics [Cambridge]Laboratoire de combinatoire et d'informatique mathématique [Montréal]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 $r = \dim (A_1)$.https://dmtcs.episciences.org/3634/pdfgraded algebrahopf algebragrothendieck groupdual graded graph[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Nantel Bergeron Thomas Lam Huilan Li Combinatorial Hopf Algebras and Towers of Algebras Discrete Mathematics & Theoretical Computer Science graded algebra hopf algebra grothendieck group dual graded graph [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Combinatorial Hopf Algebras and Towers of Algebras |
| title_full | Combinatorial Hopf Algebras and Towers of Algebras |
| title_fullStr | Combinatorial Hopf Algebras and Towers of Algebras |
| title_full_unstemmed | Combinatorial Hopf Algebras and Towers of Algebras |
| title_short | Combinatorial Hopf Algebras and Towers of Algebras |
| title_sort | combinatorial hopf algebras and towers of algebras |
| topic | graded algebra hopf algebra grothendieck group dual graded graph [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/3634/pdf |
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