Algebraic Structures on Typed Decorated Rooted Trees
Typically decorated trees are used by Bruned, Hairer, and Zambotti to describe a renormalisation process on stochastic PDEs. We here study the algebraic structures on these objects: multiple pre-Lie algebras and related operads (generalizing a result by Chapoton and Livernet), noncommutative and coc...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211441 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Algebraic Structures on Typed Decorated Rooted Trees. Loïc Foissy. SIGMA 17 (2021), 086, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862600677314789376 |
|---|---|
| author | Foissy, Loïc |
| author_facet | Foissy, Loïc |
| citation_txt | Algebraic Structures on Typed Decorated Rooted Trees. Loïc Foissy. SIGMA 17 (2021), 086, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Typically decorated trees are used by Bruned, Hairer, and Zambotti to describe a renormalisation process on stochastic PDEs. We here study the algebraic structures on these objects: multiple pre-Lie algebras and related operads (generalizing a result by Chapoton and Livernet), noncommutative and cocommutative Hopf algebras (generalizing Grossman and Larson's construction), commutative and noncocommutative Hopf algebras (generalizing Connes and Kreimer's construction), bialgebras in cointeraction (generalizing Calaque, Ebrahimi-Fard, and Manchon's result). We also define families of morphisms and, in particular, we prove that any Connes-Kreimer Hopf algebra of typed and decorated trees is isomorphic to a Connes-Kreimer Hopf algebra of non-typed and decorated trees (the set of decorations of vertices being bigger), through a contraction process, and finally obtain the Bruned-Hairer-Zambotti construction as a subquotient.
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| first_indexed | 2026-03-14T02:38:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211441 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T02:38:13Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Foissy, Loïc 2026-01-02T08:34:25Z 2021 Algebraic Structures on Typed Decorated Rooted Trees. Loïc Foissy. SIGMA 17 (2021), 086, 28 pages 1815-0659 2020 Mathematics Subject Classification: 05C05; 16T30; 18D50; 17D25 arXiv:1811.07572 https://nasplib.isofts.kiev.ua/handle/123456789/211441 https://doi.org/10.3842/SIGMA.2021.086 Typically decorated trees are used by Bruned, Hairer, and Zambotti to describe a renormalisation process on stochastic PDEs. We here study the algebraic structures on these objects: multiple pre-Lie algebras and related operads (generalizing a result by Chapoton and Livernet), noncommutative and cocommutative Hopf algebras (generalizing Grossman and Larson's construction), commutative and noncocommutative Hopf algebras (generalizing Connes and Kreimer's construction), bialgebras in cointeraction (generalizing Calaque, Ebrahimi-Fard, and Manchon's result). We also define families of morphisms and, in particular, we prove that any Connes-Kreimer Hopf algebra of typed and decorated trees is isomorphic to a Connes-Kreimer Hopf algebra of non-typed and decorated trees (the set of decorations of vertices being bigger), through a contraction process, and finally obtain the Bruned-Hairer-Zambotti construction as a subquotient. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Algebraic Structures on Typed Decorated Rooted Trees Article published earlier |
| spellingShingle | Algebraic Structures on Typed Decorated Rooted Trees Foissy, Loïc |
| title | Algebraic Structures on Typed Decorated Rooted Trees |
| title_full | Algebraic Structures on Typed Decorated Rooted Trees |
| title_fullStr | Algebraic Structures on Typed Decorated Rooted Trees |
| title_full_unstemmed | Algebraic Structures on Typed Decorated Rooted Trees |
| title_short | Algebraic Structures on Typed Decorated Rooted Trees |
| title_sort | algebraic structures on typed decorated rooted trees |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211441 |
| work_keys_str_mv | AT foissyloic algebraicstructuresontypeddecoratedrootedtrees |