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Description:
In this paper, we investigate the structure of the magic square C*-algebra 𝐴(4) of size 4. We show that a certain twisted crossed product of 𝐴(4) is isomorphic to the homogeneous C*-algebra 𝑀4 (𝐶 ($\mathbb{R}$𝑃$^3$)). Using this result, we show that 𝐴(4) is isomorphic to the fixed point algebra of 𝑀4 (𝐶 ($\mathbb{R}$𝑃$^3$)) by a certain action. From this concrete realization of 𝐴(4), we compute the K-groups of 𝐴(4) and their generators.