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Feynman graphs, rooted trees, and Ringel-Hall algebras

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

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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
Language:
English
Keywords:

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