RESEARCH ARTICLE

$C^*$-algebra generated by four projections with sum equal to 2

Yuri Savchuk

Department of Computer Science, Kyiv Taras Shevchenko University, 64 Volodymyrska st., 01033 Kyiv Ukraine

Abstract: 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.

Keywords: matrix-functions, projections, finitely generated $C^*$-algebras.

MSC: 46L05, 47L50

Language: English

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