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http://hdl.handle.net/1843/37638| Type: | Artigo de Periódico |
| Title: | Graded manifolds of type Δ and n-fold vector bundles |
| Authors: | Elizaveta Vishnyakova |
| Abstract: | Vector bundles and double vector bundles, or twofold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these structures possess a unified description using the language of supergeometry and Z-graded manifolds of degree ≤2. Indeed, a link has been established between the super and classical pictures by the geometrization process, leading to an equivalence of the category of Z-graded manifolds of degree ≤2 and the category of (double) vector bundles with additional structures. In this paper we study the geometrization process in the case of Zr-graded manifolds of type Δ, where Δ is a certain weight system and r is the rank of Δ. We establish an equivalence between a subcategory of the category of n-fold vector bundles and the category of graded manifolds of type Δ. |
| Subject: | Supervariedades (Matemática) Lie, Superálgebras de Campos vetoriais |
| language: | eng |
| metadata.dc.publisher.country: | Brasil |
| Publisher: | Universidade Federal de Minas Gerais |
| Publisher Initials: | UFMG |
| metadata.dc.publisher.department: | ICX - DEPARTAMENTO DE MATEMÁTICA |
| Rights: | Acesso Restrito |
| metadata.dc.identifier.doi: | https://doi.org/10.1007/s11005-018-1105-9 |
| URI: | http://hdl.handle.net/1843/37638 |
| Issue Date: | Feb-2019 |
| metadata.dc.url.externa: | https://link.springer.com/article/10.1007/s11005-018-1105-9 |
| metadata.dc.relation.ispartof: | Letters in Mathematical Physics |
| Appears in Collections: | Artigo de Periódico |
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