Budianti, Rita Anggraeni (2016) KAITAN ANTARA ALJABAR CUNTZ-KRIEGER O_A DAN ALJABAR CUNTZ-KRIEGER DARI GRAF E. S1 thesis, Universitas Pendidikan Indonesia.
Abstract
Diberikan n∈N, Σ={1,…,n} dan matriks A=(A(i,j))_(i,j∈Σ), A(i,j)∈{0,1} di mana setiap baris dan kolom dari A tak nol. Aljabar-C^* 〖 O〗_A dibangun oleh isometri parsial S_i≠0 ,i∈Σ pada ruang Hilbert di mana proyeksi awal Q_i=S_i^* S_i dan proyeksi akhir P_i=S_i S_i^* memenuhi relasi Cuntz-Krieger. Selanjutnya diberikan graf berarah E yang terdiri dari himpunan countable E^0,E^1 dan fungsi r,s∶E^1→E^0. Aljabar-C^* C^* (E) dibangun oleh keluarga Cuntz-Krieger E. Pada skripsi ini dibahas konstruksi aljabar Cuntz-Krieger dari graf E dan kaitannya dengan aljabar Cuntz- Krieger 〖 O〗_A . Hasilnya, matriks A pada aljabar Cuntz-Krieger 〖 O〗_A berkaitan dengan matriks sisi dan matriks titik dari graf E pada aljabar Cuntz-Krieger dari graf E. Lebih lanjut, 〖 O〗_A isomorfik ke C^* (E_A ).
Kata Kunci : Aljabar-C^*, keluarga Cuntz-Krieger, graf, matriks sisi, matriks titik.
Given n∈N, Σ={1,…,n} and a matrix A=(A(i,j))_(i,j∈Σ), A(i,j)∈{0,1} where every row and every column of A is non-zero. A C^*-algebras 〖 O〗_A generated by partial isometries S_i≠0 (i∈Σ) that act on a Hilbert space in such a way that their support projections Q_i=S_i^* S_i and their range projections P_i=S_i S_i^* satisfy the Cuntz-Krieger relations. A directed graph E consists of two countable sets E^0,E^1 and function r,s∶E^1→E^0. C^*-algebras C^* (E) generated by a Cuntz-Krieger E-family. On this study we learn how to construct a Cuntz- Krieger algebra 〖 O〗_A, Cuntz-Krieger algebra of E and how they are related to each other. The result is a matrix A on Cuntz-Krieger algebra O_A associated to edge matrix and vertex matrix of E on Cuntz-Krieger algebra of E. Furthermore, 〖 O〗_A isomorphic to C^* (E_A ).
Key words: C^*-algebras, Cuntz-Krieger family, graph, edge matrix and vertex matrix.
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| Item Type: | Thesis (S1) |
|---|---|
| Additional Information: | No. Panggil : S MAT BUD k-2016; Pembimbing : I. Rizky Rosjanuardi, II. Isnie Yusnitha |
| Uncontrolled Keywords: | Aljabar-C^*, keluarga Cuntz-Krieger, graf, matriks sisi, matriks titik. |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 |
| Depositing User: | Mrs. Neni Sumarni |
| Date Deposited: | 12 Oct 2017 03:40 |
| Last Modified: | 12 Oct 2017 03:40 |
| URI: | http://repository.upi.edu/id/eprint/27036 |
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