Characterization of Directed Graphs Representing C-Algebra of Complex Matrices

• Published in: E3S web of conferences Vol. 483; p. 3004
• Main Authors: Hidayat, Wahyu, Herlinawati, Elin
• Format: Journal Article
• Language: English
• Published: EDP Sciences 01.01.2024
• ISSN: 2267-1242; 2267-1242
• DOI: 10.1051/e3sconf/202448303004

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.