On the Representations and Characters of Cat¹-Groups and Crossed Modules
| dc.contributor.author | Davvaz, B. | |
| dc.contributor.author | Dehghani, M. A. | |
| dc.contributor.department | Other | tr_TR |
| dc.contributor.faculty | Other | tr_TR |
| dc.date.accessioned | 2021-10-25T13:45:31Z | |
| dc.date.available | 2021-10-25T13:45:31Z | |
| dc.date.issued | 2019-02-01 | |
| dc.description.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 ∑_{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. | tr_TR |
| dc.description.index | Trdizin | tr_TR |
| dc.identifier.endpage | 86 | tr_TR |
| dc.identifier.issn/e-issn | 2618-6470 | |
| dc.identifier.issue | 1 | tr_TR |
| dc.identifier.startpage | 70 | tr_TR |
| dc.identifier.uri | https://doi.org/10.31801/cfsuasmas.443623 | tr_TR |
| dc.identifier.uri | http://hdl.handle.net/20.500.12575/75730 | |
| dc.identifier.volume | 68 | tr_TR |
| dc.language.iso | en | tr_TR |
| dc.publisher | Ankara Üniversitesi | tr_TR |
| dc.relation.isversionof | 10.31801/cfsuasmas.443623 | tr_TR |
| dc.relation.journal | Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics | tr_TR |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Başka Kurum Yazarı | tr_TR |
| dc.subject | Cat¹-group | tr_TR |
| dc.subject | Crossed module | tr_TR |
| dc.subject | Chain complex | tr_TR |
| dc.title | On the Representations and Characters of Cat¹-Groups and Crossed Modules | tr_TR |
| dc.type | Article | tr_TR |