On the magic square C*-algebra of size 4
Annales mathématiques Blaise Pascal, Tome 29 (2022) no. 1, pp. 99-148.

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(P 3 )). Using this result, we show that A(4) is isomorphic to the fixed point algebra of M 4 (C(P 3 )) by a certain action. From this concrete realization of A(4), we compute the K-groups of A(4) and their generators.

Publié le :
DOI : 10.5802/ambp.408
Classification : 46L05, 46L55, 46L80
Mots clés : C*-algebra, magic square C*-algebra, twisted crossed product, K-theory
Katsura, Takeshi 1 ; Ogawa, Masahito 2 ; Takeuchi, Airi 3

1 Department of Mathematics Faculty of Science and Technology Keio University 3-14-1 Hiyoshi, Kouhoku-ku, Yokohama 223-8522 JAPAN
2 Library & Information center Yokohama City University 22-2 Seto, Kanazawa-ku, Yokohama 236-0027 JAPAN
3 Karlsruhe Institute of Technology Department of Mathematics 76128 Karlsruhe GERMANY
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Katsura, Takeshi; Ogawa, Masahito; Takeuchi, Airi. On the magic square C*-algebra of size 4. Annales mathématiques Blaise Pascal, Tome 29 (2022) no. 1, pp. 99-148. doi : 10.5802/ambp.408. http://www.numdam.org/articles/10.5802/ambp.408/

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