On the magic square C*-algebra of size 4

Takeshi Katsura; Masahito Ogawa; Airi Takeuchi

doi:10.5802/ambp.408

On the magic square C*-algebra of size 4

Takeshi Katsura, Masahito Ogawa, Airi Takeuchi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 M₄ (FORMULA PRESENT (RP³ )). Using this result, we show that A(4) is isomorphic to the fixed point algebra of M₄ (C (RP³ )) by a certain action. From this concrete realization of A(4), we compute the K-groups of A(4) and their generators.

Original language	English
Pages (from-to)	99-148
Number of pages	50
Journal	Annales Mathematiques Blaise Pascal
Volume	29
Issue number	1
DOIs	https://doi.org/10.5802/ambp.408
Publication status	Published - 2022

Keywords

46L55
46L80
C*-algebra
K-theory. 2020 Mathematics Subject Classification: 46L05
magic square C*-algebra
twisted crossed product

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

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10.5802/ambp.408

Cite this

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title = "On the magic square C*-algebra of size 4",

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 M4 (FORMULA PRESENT (RP3 )). Using this result, we show that A(4) is isomorphic to the fixed point algebra of M4 (C (RP3 )) by a certain action. From this concrete realization of A(4), we compute the K-groups of A(4) and their generators.",

keywords = "46L55, 46L80, C*-algebra, K-theory. 2020 Mathematics Subject Classification: 46L05, magic square C*-algebra, twisted crossed product",

author = "Takeshi Katsura and Masahito Ogawa and Airi Takeuchi",

note = "Funding Information: The first named author is supported by JSPS KAKENHI Grant Number JP18K03345. The third named author is supported by Masason Foundation. Keywords: C*-algebra, magic square C*-algebra, twisted crossed product, K-theory. 2020 Mathematics Subject Classification: 46L05, 46L55, 46L80. Publisher Copyright: {\textcopyright} 2022, Universite Clermont Auvergne. All rights reserved.",

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doi = "10.5802/ambp.408",

language = "English",

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pages = "99--148",

journal = "Annales Mathematiques Blaise Pascal",

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AU - Ogawa, Masahito

AU - Takeuchi, Airi

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PY - 2022

Y1 - 2022

N2 - 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 M4 (FORMULA PRESENT (RP3 )). Using this result, we show that A(4) is isomorphic to the fixed point algebra of M4 (C (RP3 )) by a certain action. From this concrete realization of A(4), we compute the K-groups of A(4) and their generators.

AB - 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 M4 (FORMULA PRESENT (RP3 )). Using this result, we show that A(4) is isomorphic to the fixed point algebra of M4 (C (RP3 )) by a certain action. From this concrete realization of A(4), we compute the K-groups of A(4) and their generators.

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KW - K-theory. 2020 Mathematics Subject Classification: 46L05

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KW - twisted crossed product

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On the magic square C*-algebra of size 4

Abstract

Keywords

ASJC Scopus subject areas

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