On the simplicity crossed polymodules
The conception of crossed modules was first expressed by Whitehead when he was working on combinatorial theory. This concept has many uses in various fields, such as category theory, algebra, and k-theory. Moreover, one of the equations that plays a very important role in mathematical problems is th...
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Tokat Gaziosmanpasa University
2023-08-01
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| Series: | Journal of New Results in Science |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3126068 |
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| author | Mohammad Ali Dehghanizadeh |
| author_facet | Mohammad Ali Dehghanizadeh |
| author_sort | Mohammad Ali Dehghanizadeh |
| collection | DOAJ |
| description | The conception of crossed modules was first expressed by Whitehead when he was working on combinatorial theory. This concept has many uses in various fields, such as category theory, algebra, and k-theory. Moreover, one of the equations that plays a very important role in mathematical problems is the Yang-Baxter equation. In fact, although it doesn't seem like it, these equations play an effective role in studies such as particle physics, statistical mechanics, quantum field theory, and quantum groups. We use crossed modules to solve them. In crossed modules, the Actor was defined by Alp. Nilpotent, Solvable, $n$-Complete, and Representations of crossed modules were studied by Dehghanizadeh and Davvaz. In studies of group theory, a simplicial group is an object. Davvaz and Alp studied simplicial polygroups, and the generalized Moore complexes. They proved the existence of a functor from the category cat$^1$-polygroups to the category of groups and, furthermore, conversely. In this paper, we provide simplicity-crossed polymodules and some of their properties. We have also presented a simple crossed polymodules theorem. |
| format | Article |
| id | doaj-art-e05acd5bfd6344698a6d26fb2db7ca8a |
| institution | Kabale University |
| issn | 1304-7981 |
| language | English |
| publishDate | 2023-08-01 |
| publisher | Tokat Gaziosmanpasa University |
| record_format | Article |
| series | Journal of New Results in Science |
| spelling | doaj-art-e05acd5bfd6344698a6d26fb2db7ca8a2025-08-20T03:44:20ZengTokat Gaziosmanpasa UniversityJournal of New Results in Science1304-79812023-08-01122869610.54187/jnrs.1293319142On the simplicity crossed polymodulesMohammad Ali Dehghanizadeh0https://orcid.org/0000-0001-6327-6416Technical and Vocational University(TVU)The conception of crossed modules was first expressed by Whitehead when he was working on combinatorial theory. This concept has many uses in various fields, such as category theory, algebra, and k-theory. Moreover, one of the equations that plays a very important role in mathematical problems is the Yang-Baxter equation. In fact, although it doesn't seem like it, these equations play an effective role in studies such as particle physics, statistical mechanics, quantum field theory, and quantum groups. We use crossed modules to solve them. In crossed modules, the Actor was defined by Alp. Nilpotent, Solvable, $n$-Complete, and Representations of crossed modules were studied by Dehghanizadeh and Davvaz. In studies of group theory, a simplicial group is an object. Davvaz and Alp studied simplicial polygroups, and the generalized Moore complexes. They proved the existence of a functor from the category cat$^1$-polygroups to the category of groups and, furthermore, conversely. In this paper, we provide simplicity-crossed polymodules and some of their properties. We have also presented a simple crossed polymodules theorem.https://dergipark.org.tr/en/download/article-file/3126068crossed modulecrossed polymodulecombinatorial homotopy |
| spellingShingle | Mohammad Ali Dehghanizadeh On the simplicity crossed polymodules Journal of New Results in Science crossed module crossed polymodule combinatorial homotopy |
| title | On the simplicity crossed polymodules |
| title_full | On the simplicity crossed polymodules |
| title_fullStr | On the simplicity crossed polymodules |
| title_full_unstemmed | On the simplicity crossed polymodules |
| title_short | On the simplicity crossed polymodules |
| title_sort | on the simplicity crossed polymodules |
| topic | crossed module crossed polymodule combinatorial homotopy |
| url | https://dergipark.org.tr/en/download/article-file/3126068 |
| work_keys_str_mv | AT mohammadalidehghanizadeh onthesimplicitycrossedpolymodules |