| Issue |
E3S Web Conf.
Volume 483, 2024
The 3rd International Seminar of Science and Technology (ISST 2023)
|
|
|---|---|---|
| Article Number | 03004 | |
| Number of page(s) | 13 | |
| Section | Trends in Mathematics and Computer Science for Sustainable Living | |
| DOI | https://doi.org/10.1051/e3sconf/202448303004 | |
| Published online | 31 January 2024 | |
Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices
Universitas Terbuka, Mathematics Department, 15437 South Tangerang, Banten, Indonesia
* Corresponding author: wahyuhidayat@ecampus.ut.ac.id
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.
© The Authors, published by EDP Sciences, 2024
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