On the magic square C*-algebra of size 4

Katsura, Takeshi; Ogawa, Masahito; Takeuchi, Airi

doi:10.5802/ambp.408

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

Annales mathématiques Blaise Pascal, Tome 29 (2022) no. 1, pp. 99-148.

Résumé

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

Publié le : 2022-09-23

DOI : 10.5802/ambp.408

Classification : 46L05, 46L55, 46L80
Mots clés : C*-algebra, magic square C*-algebra, twisted crossed product, K-theory

Affiliations des auteurs :

Katsura, Takeshi ¹ ; Ogawa, Masahito ² ; Takeuchi, Airi ³

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     title = {On the magic square {C*-algebra} of size 4},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {99--148},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
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     year = {2022},
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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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