Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable
This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg. Comm. Comput. 11 (2001), 417-436], wherein Olver uses a moving frames approach to examine the action of a group on a curve within a generalization of jet space known as multispace. Here, we seek to further study group...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212121 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable. Peter Rock. SIGMA 20 (2024), 002, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862579019660132352 |
|---|---|
| author | Rock, Peter |
| author_facet | Rock, Peter |
| citation_txt | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable. Peter Rock. SIGMA 20 (2024), 002, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg. Comm. Comput. 11 (2001), 417-436], wherein Olver uses a moving frames approach to examine the action of a group on a curve within a generalization of jet space known as multispace. Here, we seek to further study group actions on the multispace of curves by computing the infinitesimals for a given action. For the most part, we proceed formally and produce in the multispace a recursion relation that closely mimics the previously known prolongation recursion relations for infinitesimals of a group action on jet space.
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| first_indexed | 2026-03-13T16:21:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212121 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T16:21:48Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rock, Peter 2026-01-28T14:00:47Z 2024 Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable. Peter Rock. SIGMA 20 (2024), 002, 18 pages 1815-0659 2020 Mathematics Subject Classification: 53A70; 58D19 arXiv:2306.13175 https://nasplib.isofts.kiev.ua/handle/123456789/212121 https://doi.org/10.3842/SIGMA.2024.002 This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg. Comm. Comput. 11 (2001), 417-436], wherein Olver uses a moving frames approach to examine the action of a group on a curve within a generalization of jet space known as multispace. Here, we seek to further study group actions on the multispace of curves by computing the infinitesimals for a given action. For the most part, we proceed formally and produce in the multispace a recursion relation that closely mimics the previously known prolongation recursion relations for infinitesimals of a group action on jet space. The author would like to thank Dr. Jeanne Clelland for her guidance and support throughout the writing of this paper. In addition, the author would like to thank the referees for their helpful comments and suggestions, which significantly contributed to the clarity of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable Article published earlier |
| spellingShingle | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable Rock, Peter |
| title | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable |
| title_full | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable |
| title_fullStr | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable |
| title_full_unstemmed | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable |
| title_short | Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable |
| title_sort | computation of infinitesimals for a group action on a multispace of one independent variable |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212121 |
| work_keys_str_mv | AT rockpeter computationofinfinitesimalsforagroupactiononamultispaceofoneindependentvariable |