\(C^*\)-algebra generated by four projections with sum equal to 2

• Date: 2018
• Main Author: Savchuk, Yuri
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: matrix-functions; projections; finitely generated \(C^*\)-algebras; 46L05; 47L50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1004
• Journal Title: Algebra and Discrete Mathematics

We describe the \(C^*\)-algebra generated by four orthogonal projections \(p_1, p_2, p_3, p_4\), satisfying the linear relation \(p_1+p_2+p_3+p_4=2I\). The simplest realization by \(2\times 2\)-matrix-functions over the sphere \(S^2\) is given.