- Abstract:
- We construct symmetric monoidal categories $\LRF, \FD$ of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf algebras of $\LRF, \FD$, $\HH_{\LRF}, \HH_{\FD}$ are dual to the corresponding Connes-Kreimer Hopf algebras on rooted trees and Feynman graphs. We thus obtain an interpretation of the Connes-Kreimer Lie algebras on rooted trees and Feynman graphs as Ringel-Hall Lie algebras.
- Publication status:
- Published
- Publisher copy:
- 10.1007/s00220-008-0694-z
-
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- Journal:
- COMMUNICATIONS IN MATHEMATICAL PHYSICS
- Volume:
- 289
- Issue:
- 2
- Pages:
- 561-577
- Publication date:
- 2008-06-06
- DOI:
- EISSN:
-
1432-0916
- ISSN:
-
0010-3616
- URN:
-
uuid:29e42853-50ef-4719-9140-8aca3e939434
- Source identifiers:
-
199444
- Local pid:
- pubs:199444
- Copyright date:
- 2008
Journal article
Feynman graphs, rooted trees, and Ringel-Hall algebras
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