Nugroho Dwi Widodo, - (2021) KAITAN ALJABAR LINTASAN COHN DENGAN ALJABAR-C^* MELALUI ALJABAR LINTASAN LEAVITT. S1 thesis, Universitas Pendidikan Indonesia.
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Abstract
Untuk sembarang graf berarah E dan lapangan K kita dapat membuat sebuah aljabar lintasan Leavitt yang berasal dari aljabar lintasan Cohn yaitu C_K (E). Dari hasil investigasi Abrams, Pere Ara, dan Molina, dapat ditentukan suatu graf berarah F sedemikian sehingga aljabar lintasan Cohn isomorfik terhadap suatu aljabar lintasan Leavitt yaitu C_K (E)≅L_K (F). Ketika lapangan K=C, kita punya berdasarkan pembahasan oleh Tomforde, bahwa L_C (F) isomorfik dengan subaljabar-* padat C^* (F) secara khusus L_C (F)≅C^* (F). Dari kedua kaitan tersebut, bagaimanakah hubungan antara aljabar lintasan Cohn dan aljabar-C^*?. Melalui masing-masing kaitan antara aljabar lintasan Cohn dan aljabar-C^* dengan aljabar lintasan Leavitt, diperoleh C_C (E)≅C^* (F), sehingga aljabar lintasan Cohn dapat dipandang sebagai aljabar graf dari C^* (F), yaitu aljabar-C^* untuk suatu graf berarah F dengan graf F yang merupakan graf yang dibentuk dari graf berarah E dengan menambahkan sisi dan simpul berdasarkan ketentuan tertentu. For any directed graph E and any field K we can produce Leavitt path algebra from Cohn path algebra C_K (E). The result of investigation by Abrams, Pere Ara, dan Molina, we could choose a directed graph F such that Cohn path algebra and Leavitt path algebra are isomorphic which is C_K (E)≅L_K (F). As field K=C, according Tomforde’s discussion, that Leavitt path algebra is isomorphic to a dense *-subalgebra, in particular L_C (F)≅C^* (F). Based on both connection, is there any connection between Cohn path algebra and C^*-algebra?. Through each connection between Cohn path algebra and C^*-algebra with Leavitt path algebra, we obtained C_C (E)≅C^* (F), so that Cohn path algebra could be viewed as graph algebra from C^* (F), which is C^*-algebra for a directed graph F, with graph F was graph made from directed graph E by adding some edges and vertex based on certain conditions.
| Item Type: | Thesis (S1) |
|---|---|
| Uncontrolled Keywords: | Aljabar graf, aljabar-C^*, aljabar lintasan Leavitt, aljabar lintasan Cohn |
| Subjects: | L Education > L Education (General) Q Science > QA Mathematics |
| Divisions: | Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Jurusan Pendidikan Matematika |
| Depositing User: | Nugroho Dwi Widodo |
| Date Deposited: | 06 Sep 2021 07:54 |
| Last Modified: | 06 Sep 2021 07:54 |
| URI: | http://repository.upi.edu/id/eprint/64734 |
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