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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 68 Issue: 1

On the Representations and Characters of Cat¹-Groups and Crossed Modules

M. A. Dehghani0000-0001-6327-6416
B. Davvaz0000-0003-1941-5372
Pages
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Publication Date
2019-02-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, if χ=(G,M,μ,∂) is a finite crossed module and ψ is an irreducible character of χ, then

📌 3 Key Takeaways

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Objective & Hypothesis:Let G be a group and V a K-vector space.
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Key Findings & Data:A K-linear representation of G with representation space V is a homomorphism φ:G→GL(V).
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Conclusion & Impact:Also, if χ=(G,M,μ,∂) is a finite crossed module and ψ is an irreducible character of χ, then
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cat¹-group · crossed module · chain complex

Abstract

Let G be a group and V a K-vector space. A K-linear representation of G with representation space V is a homomorphism φ:G→GL(V). The dimension of V is called the degree of φ. If φ is a representation of G, then the character φ is defined for g∈G as ψ_{g}(φ)=Tr(φ(g)). In this paper we study the representations and characters of cat¹-groups and crossed modules. We show that for class functions ψ₁ and ψ₂ of crossed module χ=(G,M,μ,∂), the inner product is Hermitian. Also, if χ=(G,M,μ,∂) is a finite crossed module and ψ is an irreducible character of χ, then

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Cite This Article

Dehghani, M. A., Davvaz, B. (2019). On the Representations and Characters of Cat¹-Groups and Crossed Modules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 1. https://doi.org/10.31801/cfsuasmas.443623

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