Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices
Quantum mechanics is a study that plays a major role in determining the biological intelligence of Artificial Intelligence (AI). Point particle systems in quantum mechanics can be explained using C*-Algebra which is called CAR-algebra. There is a special case in the CAR-algebra which is isomorphic t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2024-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2024/13/e3sconf_isst2024_03004.pdf |
| _version_ | 1797333989412831232 |
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| author | Hidayat Wahyu Herlinawati Elin |
| author_facet | Hidayat Wahyu Herlinawati Elin |
| author_sort | Hidayat Wahyu |
| collection | DOAJ |
| description | Quantum mechanics is a study that plays a major role in determining the biological intelligence of Artificial Intelligence (AI). Point particle systems in quantum mechanics can be explained using C*-Algebra which is called CAR-algebra. There is a special case in the CAR-algebra which is isomorphic to the C*-algebra of complex matrices. On the other hand, C*-algebras of direct sum of complex matrix spaces is isomorphic to C*-algebra constructed by orthogonal projection and partial isometries operators via the Cuntz-Krieger relations of a directed graph. This article will provide a basis for the relationship between quantum mechanics and graphs through a discussion of the characterization of graphs that can represent C*-algebra of complex matrices. It is found that C*-algebra complex matrices n × n is a directed graph without cycles with n – 1 arrows, a single source, and has n path from the source. |
| first_indexed | 2024-03-08T08:14:09Z |
| format | Article |
| id | doaj.art-19d3ca4304d941d7a9b6c6f1667fe9d0 |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-03-08T08:14:09Z |
| publishDate | 2024-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-19d3ca4304d941d7a9b6c6f1667fe9d02024-02-02T07:57:30ZengEDP SciencesE3S Web of Conferences2267-12422024-01-014830300410.1051/e3sconf/202448303004e3sconf_isst2024_03004Characterization of Directed Graphs Representing C*-Algebra of Complex MatricesHidayat Wahyu0Herlinawati Elin1Universitas Terbuka, Mathematics DepartmentUniversitas Terbuka, Mathematics DepartmentQuantum mechanics is a study that plays a major role in determining the biological intelligence of Artificial Intelligence (AI). Point particle systems in quantum mechanics can be explained using C*-Algebra which is called CAR-algebra. There is a special case in the CAR-algebra which is isomorphic to the C*-algebra of complex matrices. On the other hand, C*-algebras of direct sum of complex matrix spaces is isomorphic to C*-algebra constructed by orthogonal projection and partial isometries operators via the Cuntz-Krieger relations of a directed graph. This article will provide a basis for the relationship between quantum mechanics and graphs through a discussion of the characterization of graphs that can represent C*-algebra of complex matrices. It is found that C*-algebra complex matrices n × n is a directed graph without cycles with n – 1 arrows, a single source, and has n path from the source.https://www.e3s-conferences.org/articles/e3sconf/pdf/2024/13/e3sconf_isst2024_03004.pdf |
| spellingShingle | Hidayat Wahyu Herlinawati Elin Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices E3S Web of Conferences |
| title | Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices |
| title_full | Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices |
| title_fullStr | Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices |
| title_full_unstemmed | Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices |
| title_short | Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices |
| title_sort | characterization of directed graphs representing c algebra of complex matrices |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2024/13/e3sconf_isst2024_03004.pdf |
| work_keys_str_mv | AT hidayatwahyu characterizationofdirectedgraphsrepresentingcalgebraofcomplexmatrices AT herlinawatielin characterizationofdirectedgraphsrepresentingcalgebraofcomplexmatrices |