Browsing by Author "Davvaz, B."

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    On the Representations and Characters of Cat¹-Groups and Crossed Modules
    (Ankara Üniversitesi, 2019-02-01) Davvaz, B.; Dehghani, M. A.; Other; Other
    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 ∑_{m∈M,g∈G}ψ(m,g)ψ(m⁻¹,g⁻¹)=|G||M|. Moreover, we present some examples of the character tables of crossed modules.
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    Soft semi-topological polygroups
    (Ankara Üniversitesi, 2022) Davvaz, B.; Other; Other
    By removing the condition that the inverse function is continuous in soft topological polygroups, we will have less constraint to obtain the results. We offer different definitions for soft topological polygroups and eliminate the inverse function continuity condition to have more freedom of action.