An AF Algebra Associated with the Farey Tessellation
An AF Algebra Associated with the Farey Tessellation
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与 Farey 曲面细分相关的 AF 代数
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
F. Boca
中科院分区：
文献类型：
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作者：
F. Boca
Abstract We associate with the Farey tessellation of the upper half-plane an $ ext{AF}$ algebra $mathfrak{A}$ encoding the “cutting sequences” that define vertical geodesics. The Effros–Shen $ ext{AF}$ algebras arise as quotients of $mathfrak{A}$ . Using the path algebra model for $ ext{AF}$ algebras we construct, for each $ au ,,in ,,left( 0
ight.,left. frac{1}{4}
ight]$ , projections $({{E}_{n}})$ in $mathfrak{A}$ such that ${{E}_{n}}{{E}_{npm 1}}Ele au {{E}_{n}}$ .
Abstract We associate with the Farey tessellation of the upper half-plane an $ ext{AF}$ algebra $mathfrak{A}$ encoding the “cutting sequences” that define vertical geodesics. The Effros–Shen $ ext{AF}$ algebras arise as quotients of $mathfrak{A}$ . Using the path algebra model for $ ext{AF}$ algebras we construct, for each $ au ,,in ,,left( 0
ight.,left. frac{1}{4}
ight]$ , projections $({{E}_{n}})$ in $mathfrak{A}$ such that ${{E}_{n}}{{E}_{npm 1}}Ele au {{E}_{n}}$ .