K-theory of quasicrystals, gap labelling: the octagonal lattice

被引：16

作者：

Bellissard, J

Contensou, E

Legrand, A

机构：

[1] Univ Toulouse 3, Inst Univ France, F-31062 Toulouse 4, France

[2] Univ Toulouse 3, Inst Rech Syst Atom & Mol Complexes, F-31062 Toulouse, France

[3] Univ Toulouse 3, CNRS, UMR 8850, Lab Math Emile Picard, F-31062 Toulouse 4, France

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1998年 / 326卷 / 02期

关键词：

D O I：

10.1016/S0764-4442(97)89470-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the C-*-algebra of a quasicrystal constructed by the strip and projection method is Morita-equivalent to a crossed product. Its K-theory is thus obtained as limit of the Kasparov spectral sequence. When the quasicrystal is 2-dimensional, the spectral sequence degenerates and leads to the gap labelling for rite octagonal quasicrystal.

引用

页码：197 / 200

页数：4

共 11 条

[1]

BELLISSARD J, 1992, GAP LABELLING THEORE

[2]

BELLISSARD J, 1997, UNPUB K THEORY QUASI

[3]

BELLISSARD J, 1986, LECTURE NOTES PHYSIC, V257, P99

[4]

Bratteli O., 1974, Journal of Functional Analysis, V16, P192, DOI 10.1016/0022-1236(74)90063-9

[5]

Contensou E, 1997, CR ACAD SCI I-MATH, V324, P293

[6] EQUIVARIANT KK-THEORY AND THE NOVIKOV-CONJECTURE [J].

KASPAROV, GG .

INVENTIONES MATHEMATICAE, 1988, 91 (01) :147-201

[7] QUASI-PERIODIC PATTERNS AND ICOSAHEDRAL SYMMETRY [J].

KATZ, A ;

DUNEAU, M .

JOURNAL DE PHYSIQUE, 1986, 47 (02) :181-196

[8]

MUHLY PS, 1987, J OPERAT THEOR, V17, P3

[9]

Renault J., 1980, LECT NOTES MATH, V793

[10]

RIEFFEL MA, 1982, P SYMP PURE MATH, V38, P299

← 1 2 →