Graded manifolds of type and n-fold vector bundles

Author(s)

Vishnyakova, Elizaveta

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

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 , 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