Graded manifolds of type and n-fold vector bundles

Autor(es)

Vishnyakova, Elizaveta

• Tipo de documento: Artigo Científico
• Fonte: LETTERS IN MATHEMATICAL PHYSICS; v. 109, n. 2, p. 243-293, FEB 2019.
• Citações Web of Science: 0

Resumo

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 , where is a certain weight system and r is the rank of . We establish an equivalence between a subcategory of the category of n-fold vector bundles and the category of graded manifolds of type Delta. (AU)

• Processo FAPESP: 15/15901-9 - O formalismo de bracket derivado em álgebra e geometria, módulos de Gelfand-Tsetlin para superálgebras de Lie
• Beneficiário: Elizaveta Gennadievna Vishnyakova
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado