2-Representations of Lie 2-groups and 2-Vector Bundles

2022/08/22 by Zhen Huan, Huan, Zhen
Mathematics · Medicine · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2208.10042

openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Murray, Roberts and Wockel showed that there is no strict model of the string 2-group using the free loop group. Instead, they construct the next best thing, a coherent model for the string 2-group using the free loop group, with explicit formulas for all structure. Based on their expectations, we build a category of 2-representations for coherent Lie 2-groups and some concrete examples. We also discuss the relation between this category of 2-representations and the category of representations. In addition, we construct a model of equivariant 2-vector bundles. At the end, we discuss the adjoint action on the string 2-representations.

Related

• A representation of the string 2-group
• From Loop Groups to 2-Groups
• Explicit String bundles
• The geometry of unitary 2-representations of finite groups and their 2-characters
• Lie 2-Algebras