Unbounded representations of q-deformation of Cuntz algebra

被引：2

作者：

Ostrovskyi, Vasyl ^{[1
]}

Proskurin, Daniil ^{[2
]}

Turowska, Lyudmila ^{[3
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, Kiev, Ukraine

[2] Kyiv Natl Taras Shevchenko Univ, Fac Cybernet, Kiev, Ukraine

[3] Chalmers, Dept Math, S-41296 Gothenburg, Sweden

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2008年 / 85卷 / 2-3期

基金：

瑞典研究理事会;

关键词：

Cuntz algebra; deformed commutation relations; unbounded representation;

D O I：

10.1007/s11005-008-0256-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study a deformation of the Cuntz-Toeplitz C*-algebra determined by the relations a(i)(*)ai = 1 + qa(i)a(i)(*), a(i)(*)a(j) = 0. We define its well-behaved unbounded *-representations and classify all irreducible ones up to unitary equivalence.

引用

页码：147 / 162

页数：16

共 24 条

[1] Algebras of unbounded operators and physical applications: A survey [J].

Bagarello, F. .

REVIEWS IN MATHEMATICAL PHYSICS, 2007, 19 (03) :231-271

[2]

BARUT AO, 1986, THEORY GROUP REPRESE

[3] THE QUANTUM GROUP SUQ(2) AND A Q-ANALOGUE OF THE BOSON OPERATORS [J].

BIEDENHARN, LC .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (18) :L873-L878

[4] AN EXAMPLE OF A GENERALIZED BROWNIAN-MOTION [J].

BOZEJKO, M ;

SPEICHER, R .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 137 (03) :519-531

[5] COMPLETELY POSITIVE MAPS ON COXETER GROUPS, DEFORMED COMMUTATION RELATIONS, AND OPERATOR-SPACES [J].

BOZEJKO, M ;

SPEICHER, R .

MATHEMATISCHE ANNALEN, 1994, 300 (01) :97-120

[6]

BRATTELI O, 2004, MEM AM MATH SOC, V797

[7] SIMPLE CSTAR-ALGEBRAS GENERATED BY ISOMETRIES [J].

CUNTZ, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 57 (02) :173-185

[8] GENERALIZED DEFORMED OSCILLATOR AND NONLINEAR ALGEBRAS [J].

DASKALOYANNIS, C .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (15) :L789-L794

[9]

FLATO M, 1972, ANN SCI ECOLE NORM S, V5, P423

[10] PARTICLES WITH SMALL VIOLATIONS OF FERMI OR BOSE STATISTICS [J].

GREENBERG, OW .

PHYSICAL REVIEW D, 1991, 43 (12) :4111-4120

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