2021•Repository KITopen (Karlsruhe Institute of Technology)Open access
On the magic square C*-algebra of size 4
Takeshi Katsura, Masahito Ogawa, Airi Takeuchi
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Abstract
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 $M_4(C(\mathbb{R} P^3))$. Using this result, we show that $A(4)$ is isomorphic to the fixed point algebra of $M_4(C(\mathbb{R} P^3))$ by a certain action. From this concrete realization of $A(4)$, we compute the K-groups of $A(4)$ and their generators.