On the representations of 2-groups in Baez-Crans 2-vector spaces

2016/07/18 by Benjamín Alarcón Heredia, Heredia, Benjamín Alarcón, Josep Elgueta +1
Mathematics · #18D05 #18D10 #20L05 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #math.CT #math.RT #msc:18D05 #msc:18D10 #msc:20L05

paper · pdf · doi:10.48550/arxiv.1607.04986

9 pages

arxiv created 2016/07/18 · arxiv updated 2016/07/19

Abstract

We prove that the theory of representations of a finite 2-group \mathbbG in Baez-Crans 2-vector spaces over a field k of characteristic zero essentially reduces to the theory of k-linear representations of the group of isomorphism classes of objects of \mathbbG, the remaining homotopy invariants of \mathbbG playing no role. It is also argued that a similar result is expected to hold for topological representations of compact topological 2-groups in suitable topological Baez-Crans 2-vector spaces.

Related

• Algebraic groups over a 2-dimensional local field: some further constructions
• Representations of algebraic groups over a 2-dimensional local field
• Representations of 2-transitive topological groups
• On the restriction of representations of \GL₂(F) to a Borel subgroup
• 2-Groups, 2-Characters, and Burnside Rings