Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras
We review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a generalized discrete version of the Magnus expansion. We also systematically derive the discrete analogue of the pre-Lie Magnus expansion and express the elements of the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214177 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras. Anastasia Doikou. SIGMA 21 (2025), 105, 32 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862680985985875968 |
|---|---|
| author | Doikou, Anastasia |
| author_facet | Doikou, Anastasia |
| citation_txt | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras. Anastasia Doikou. SIGMA 21 (2025), 105, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a generalized discrete version of the Magnus expansion. We also systematically derive the discrete analogue of the pre-Lie Magnus expansion and express the elements of the discrete Dyson series in terms of a tridendriform algebra binary operation. In the generic discrete case, extra significant terms that are absent in the continuous or the linear discrete case appear in both Dyson and Magnus expansions. Based on the rigorous discrete derivation, key links between quantum algebras, tridendriform, and pre-Lie algebras are then established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras. The continuous limit, as expected, provides the corresponding non-local charges of the Yangian as members of the pre-Lie Magnus expansion.
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| first_indexed | 2026-03-17T00:47:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214177 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T00:47:13Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Doikou, Anastasia 2026-02-20T07:52:36Z 2025 Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras. Anastasia Doikou. SIGMA 21 (2025), 105, 32 pages 1815-0659 2020 Mathematics Subject Classification: 16T05; 17D99; 81R50 arXiv:2211.00451 https://nasplib.isofts.kiev.ua/handle/123456789/214177 https://doi.org/10.3842/SIGMA.2025.105 We review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a generalized discrete version of the Magnus expansion. We also systematically derive the discrete analogue of the pre-Lie Magnus expansion and express the elements of the discrete Dyson series in terms of a tridendriform algebra binary operation. In the generic discrete case, extra significant terms that are absent in the continuous or the linear discrete case appear in both Dyson and Magnus expansions. Based on the rigorous discrete derivation, key links between quantum algebras, tridendriform, and pre-Lie algebras are then established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras. The continuous limit, as expected, provides the corresponding non-local charges of the Yangian as members of the pre-Lie Magnus expansion. I would like to thank the anonymous referees for their constructive comments and suggestions. Support from the EPSRC research grant EP/V008129/1 is acknowledged. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras Article published earlier |
| spellingShingle | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras Doikou, Anastasia |
| title | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras |
| title_full | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras |
| title_fullStr | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras |
| title_full_unstemmed | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras |
| title_short | Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras |
| title_sort | quantum groups, discrete magnus expansion, pre-lie and tridendriform algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214177 |
| work_keys_str_mv | AT doikouanastasia quantumgroupsdiscretemagnusexpansionprelieandtridendriformalgebras |