Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces
Associated with a symmetric space, there is a canonical connection with zero torsion and parallel curvature. This connection acts as a binary operator on the vector space of smooth sections of the tangent bundle, and it is linear with respect to the real numbers. Thus, the smooth section of the tang...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| 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/123456789/212352 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces. Hans Z. Munthe-Kaas and Jonatan Stava. SIGMA 20 (2024), 068, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712271432581120 |
|---|---|
| author | Munthe-Kaas, Hans Z. Stava, Jonatan |
| author_facet | Munthe-Kaas, Hans Z. Stava, Jonatan |
| citation_txt | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces. Hans Z. Munthe-Kaas and Jonatan Stava. SIGMA 20 (2024), 068, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Associated with a symmetric space, there is a canonical connection with zero torsion and parallel curvature. This connection acts as a binary operator on the vector space of smooth sections of the tangent bundle, and it is linear with respect to the real numbers. Thus, the smooth section of the tangent bundle together with the connection forms an algebra we call the connection algebra. The constraints of zero torsion and constant curvature make the connection algebra into a Lie admissible triple algebra. This is a type of algebra that generalises pre-Lie algebras, and it can be embedded into a post-Lie algebra in a canonical way that generalises the canonical embedding of Lie triple systems into Lie algebras. The free Lie admissible triple algebra can be described by incorporating triple-brackets into the leaves of rooted (non-planar) trees.
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| first_indexed | 2026-03-19T18:13:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212352 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T18:13:04Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Munthe-Kaas, Hans Z. Stava, Jonatan 2026-02-05T09:55:53Z 2024 Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces. Hans Z. Munthe-Kaas and Jonatan Stava. SIGMA 20 (2024), 068, 28 pages 1815-0659 2020 Mathematics Subject Classification: 53C05; 17D25; 05C05; 53C35 arXiv:2306.15582 https://nasplib.isofts.kiev.ua/handle/123456789/212352 https://doi.org/10.3842/SIGMA.2024.068 Associated with a symmetric space, there is a canonical connection with zero torsion and parallel curvature. This connection acts as a binary operator on the vector space of smooth sections of the tangent bundle, and it is linear with respect to the real numbers. Thus, the smooth section of the tangent bundle together with the connection forms an algebra we call the connection algebra. The constraints of zero torsion and constant curvature make the connection algebra into a Lie admissible triple algebra. This is a type of algebra that generalises pre-Lie algebras, and it can be embedded into a post-Lie algebra in a canonical way that generalises the canonical embedding of Lie triple systems into Lie algebras. The free Lie admissible triple algebra can be described by incorporating triple-brackets into the leaves of rooted (non-planar) trees. The authors are supported by the Research Council of Norway through the project 302831 Computational Dynamics and Stochastics on Manifolds (CODYSMA). Thanks to Kristoffer Føllesdal for early discussions on this research. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces Article published earlier |
| spellingShingle | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces Munthe-Kaas, Hans Z. Stava, Jonatan |
| title | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces |
| title_full | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces |
| title_fullStr | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces |
| title_full_unstemmed | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces |
| title_short | Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces |
| title_sort | lie admissible triple algebras: the connection algebra of symmetric spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212352 |
| work_keys_str_mv | AT munthekaashansz lieadmissibletriplealgebrastheconnectionalgebraofsymmetricspaces AT stavajonatan lieadmissibletriplealgebrastheconnectionalgebraofsymmetricspaces |