Regular F -manifolds with eventual identities
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917807719972864 |
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| author | Perletti, Sara Strachan, Ian A. B. |
| author_facet | Perletti, Sara Strachan, Ian A. B. |
| contents | Given an F-manifold one may construct a dual multiplication (generalizing the idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity, the definition of which ensure that the dual object is also an F-manifold. In this paper we solve the equations for an eventual identity for a regular (so non-semi-simple) F-manifold and construct a dual coordinate system in which dual multiplication is preserved. As an application, families of Nijenhuis operators are constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regular F -manifolds with eventual identities Perletti, Sara Strachan, Ian A. B. Differential Geometry Exactly Solvable and Integrable Systems 53D45 Given an F-manifold one may construct a dual multiplication (generalizing the idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity, the definition of which ensure that the dual object is also an F-manifold. In this paper we solve the equations for an eventual identity for a regular (so non-semi-simple) F-manifold and construct a dual coordinate system in which dual multiplication is preserved. As an application, families of Nijenhuis operators are constructed. |
| title | Regular F -manifolds with eventual identities |
| topic | Differential Geometry Exactly Solvable and Integrable Systems 53D45 |
| url | https://arxiv.org/abs/2407.06368 |