On the Homomorphisms of the Lie Groups and
We first construct all the homomorphisms from the Heisenberg group to the 3-sphere. Also, defining a topology on these homomorphisms, we regard the set of these homomorphisms as a topological space. Next, using the kernels of homomorphisms, we define an equivalence relation on this topological space...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/645848 |
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| _version_ | 1832567367411957760 |
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| author | Fatma Özdemir Hasan Özekes |
| author_facet | Fatma Özdemir Hasan Özekes |
| author_sort | Fatma Özdemir |
| collection | DOAJ |
| description | We first construct all the homomorphisms from the Heisenberg group to the 3-sphere. Also, defining a topology on these homomorphisms, we regard the set of these homomorphisms as a topological space. Next, using the kernels of homomorphisms, we define an equivalence relation on this topological space. We finally show that the quotient space is a topological group which
is isomorphic to . |
| format | Article |
| id | doaj-art-49c29c8fed3e4d298d93a72280e86e02 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-49c29c8fed3e4d298d93a72280e86e022025-02-03T01:01:36ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/645848645848On the Homomorphisms of the Lie Groups andFatma Özdemir0Hasan Özekes1Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak, 34469 Istanbul, TurkeyDepartment of Mathematics, Faculty of Science and Letters, Okan University, 34959 Istanbul, TurkeyWe first construct all the homomorphisms from the Heisenberg group to the 3-sphere. Also, defining a topology on these homomorphisms, we regard the set of these homomorphisms as a topological space. Next, using the kernels of homomorphisms, we define an equivalence relation on this topological space. We finally show that the quotient space is a topological group which is isomorphic to .http://dx.doi.org/10.1155/2013/645848 |
| spellingShingle | Fatma Özdemir Hasan Özekes On the Homomorphisms of the Lie Groups and Abstract and Applied Analysis |
| title | On the Homomorphisms of the Lie Groups and |
| title_full | On the Homomorphisms of the Lie Groups and |
| title_fullStr | On the Homomorphisms of the Lie Groups and |
| title_full_unstemmed | On the Homomorphisms of the Lie Groups and |
| title_short | On the Homomorphisms of the Lie Groups and |
| title_sort | on the homomorphisms of the lie groups and |
| url | http://dx.doi.org/10.1155/2013/645848 |
| work_keys_str_mv | AT fatmaozdemir onthehomomorphismsoftheliegroupsand AT hasanozekes onthehomomorphismsoftheliegroupsand |