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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Graded manifolds of type and n-fold vector bundles

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Vishnyakova, Elizaveta
Total Authors: 1
Document type: Journal article
Source: LETTERS IN MATHEMATICAL PHYSICS; v. 109, n. 2, p. 243-293, FEB 2019.
Web of Science Citations: 0

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)

FAPESP's process: 15/15901-9 - Derived bracket formalism in algebra and geometry and Gelfand-Tsetlin modules for Lie superalgebras
Grantee:Elizaveta Gennadievna Vishnyakova
Support Opportunities: Scholarships in Brazil - Post-Doctoral