Reduction of Lie and Courant Algebroids and Application to Double Vector Bundles

by David Kern
Doctoral thesis
Date of Examination:2023-12-18
Date of issue:2024-05-17
Advisor:Prof. Dr. Madeleine Jotz Lean
Referee:Prof. Dr. Madeleine Jotz Lean
Referee:Prof. Dr. Chenchang Zhu
Persistent Address: http://dx.doi.org/10.53846/goediss-10499

 

 

Files in this item

Name:Thesis.pdf
Size:1.41Mb
Format:PDF

The following license files are associated with this item:

Abstract

English

In this thesis we evaluate the reduction procedure of Poisson manifolds and apply it to structures closely related to them such as Lie (bi-)algebroids, Courant algebroids and Lie-Rinehart algebras. Moreover, we apply this approach also to double vector bundles and their variants, such as metric double vector bundles, VB-algebroids and VB-Courant algebroids. Finally, we give the reduction of Lie (bi-)algebroids in terms of graded manifolds of degree 1.
Keywords: Differential geometry; Symplectic geometry
 
Statistik