Some Computational Results on Koszul-Vinberg Cochain Complexes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910426651951104 |
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| author | Liu, Hanwen Zhang, Jun |
| author_facet | Liu, Hanwen Zhang, Jun |
| contents | An affine connection is said to be flat if its curvature tensor vanishes identically. Koszul-Vinberg (KV for abbreviation) cohomology has been invoked to study the deformation theory of flat and torsion-free affine connections on tangent bundle. In this Note, we compute explicitly the differentials of various specific KV cochains, and study their relation to classical objects in information geometry, including deformations associated with projective and dual-projective transformations of a flat and torsion-free affine connection. As an application, we also give a simple yet non-trivial example of a KV algebra of which second cohomology group does not vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some Computational Results on Koszul-Vinberg Cochain Complexes Liu, Hanwen Zhang, Jun Differential Geometry Information Theory An affine connection is said to be flat if its curvature tensor vanishes identically. Koszul-Vinberg (KV for abbreviation) cohomology has been invoked to study the deformation theory of flat and torsion-free affine connections on tangent bundle. In this Note, we compute explicitly the differentials of various specific KV cochains, and study their relation to classical objects in information geometry, including deformations associated with projective and dual-projective transformations of a flat and torsion-free affine connection. As an application, we also give a simple yet non-trivial example of a KV algebra of which second cohomology group does not vanish. |
| title | Some Computational Results on Koszul-Vinberg Cochain Complexes |
| topic | Differential Geometry Information Theory |
| url | https://arxiv.org/abs/2404.18344 |