On the magic square C*-algebra of size 4

Abstract

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