Annales Mathématiques
Blaise Pascal
no. 1
On the magic square C*-algebra of size 4
Takeshi Katsura1 ; Masahito Ogawa2 ; Airi Takeuchi3
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.

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(ℝP 3 )). Using this result, we show that A(4) is isomorphic to the fixed point algebra of M 4 (C(ℝP 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

Takeshi Katsura 1 ; Masahito Ogawa 2 ; Airi Takeuchi 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Takeshi Katsura; Masahito Ogawa; Airi Takeuchi. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.408/

[1] Teodor Banica; Julien Bichon Quantum groups acting on 4 points, J. Reine Angew. Math., Volume 626 (2009), pp. 75-114 | DOI | MR | Zbl

[2] Teodor Banica; Benoît Collins Integration over the Pauli quantum group, J. Geom. Phys., Volume 58 (2008) no. 8, pp. 942-961 | DOI | MR | Zbl

[3] Teodor Banica; Sergiu Moroianu On the structure of quantum permutation groups, Proc. Am. Math. Soc., Volume 135 (2007) no. 1, pp. 21-29 | DOI | MR | Zbl

[4] Julien Bichon; Robert Yuncken Quantum subgroups of the compact quantum group SU -1 (3), Bull. Lond. Math. Soc., Volume 46 (2014) no. 2, pp. 315-328 | DOI | MR | Zbl

[5] Nathanial P. Brown; Narutaka Ozawa C * -algebras and finite-dimensional approximations, Graduate Studies in Mathematics, 88, American Mathematical Society, 2008 | Zbl

[6] S. Osugi The homology theory of quotient spaces of the spheres by the action of the finite groups, 2018 (Master thesis, Keio University)

[7] Mikael Rørdam; F. Larsen; Niels Laustsen An introduction to K-theory for C * -algebras, London Mathematical Society Student Texts, 49, Cambridge University Press, 2000

[8] Christian Voigt On the structure of quantum automorphism groups, J. Reine Angew. Math., Volume 732 (2017), pp. 255-273 | DOI | MR | Zbl

[9] Shuzhou Wang Quantum symmetry groups of finite spaces, Commun. Math. Phys., Volume 195 (1998) no. 1, pp. 195-211 | DOI | MR | Zbl

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