On the Cohomology of Topological Semigroups
In this short note, we give some new results on continuous bounded cohomology groups of topological semigroups with values in complex field. We show that the second continuous bounded cohomology group of a compact metrizable semigroup, is a Banach space. Also, we study cohomology groups of amenable...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2019-09-01
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| Series: | Communications in Advanced Mathematical Sciences |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/820348 |
| _version_ | 1797294237730996224 |
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| author | Maysam Maysami Sadr Danial Bouzarjomehri Amnieh |
| author_facet | Maysam Maysami Sadr Danial Bouzarjomehri Amnieh |
| author_sort | Maysam Maysami Sadr |
| collection | DOAJ |
| description | In this short note, we give some new results on continuous bounded cohomology groups of topological semigroups with values in complex field. We show that the second continuous bounded cohomology group of a compact metrizable semigroup, is a Banach space. Also, we study cohomology groups of amenable topological semigroups, and we show that cohomology groups of rank greater than one of a compact left or right amenable semigroup, are trivial. Also, we give some examples and applications about topological lattices. |
| first_indexed | 2024-03-07T21:27:20Z |
| format | Article |
| id | doaj.art-e947efa46a8f48d49a59c2e61bb7506b |
| institution | Directory Open Access Journal |
| issn | 2651-4001 |
| language | English |
| last_indexed | 2024-03-07T21:27:20Z |
| publishDate | 2019-09-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj.art-e947efa46a8f48d49a59c2e61bb7506b2024-02-27T04:36:36ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012019-09-012320621210.33434/cams.5157111225On the Cohomology of Topological SemigroupsMaysam Maysami Sadr0Danial Bouzarjomehri Amnieh1Institute for Advanced Studies in Basic Sciences (IASBS)Institute for Advanced Studies in Basic Sciences (IASBS)In this short note, we give some new results on continuous bounded cohomology groups of topological semigroups with values in complex field. We show that the second continuous bounded cohomology group of a compact metrizable semigroup, is a Banach space. Also, we study cohomology groups of amenable topological semigroups, and we show that cohomology groups of rank greater than one of a compact left or right amenable semigroup, are trivial. Also, we give some examples and applications about topological lattices.https://dergipark.org.tr/tr/download/article-file/820348topological semigroupbounded cohomologybanach homology |
| spellingShingle | Maysam Maysami Sadr Danial Bouzarjomehri Amnieh On the Cohomology of Topological Semigroups Communications in Advanced Mathematical Sciences topological semigroup bounded cohomology banach homology |
| title | On the Cohomology of Topological Semigroups |
| title_full | On the Cohomology of Topological Semigroups |
| title_fullStr | On the Cohomology of Topological Semigroups |
| title_full_unstemmed | On the Cohomology of Topological Semigroups |
| title_short | On the Cohomology of Topological Semigroups |
| title_sort | on the cohomology of topological semigroups |
| topic | topological semigroup bounded cohomology banach homology |
| url | https://dergipark.org.tr/tr/download/article-file/820348 |
| work_keys_str_mv | AT maysammaysamisadr onthecohomologyoftopologicalsemigroups AT danialbouzarjomehriamnieh onthecohomologyoftopologicalsemigroups |