OPERATOR ALGEBRAS OF HIGHER RANK NUMERICAL SEMIGROUPS

被引：0

作者：

Kakariadis, Evgenios T. A. ^{[1
]}

Katsoulis, Elias G. ^{[2
]}

Li, Xin ^{[3
]}

机构：

[1] Newcastle Univ, Sch Math Stat & Phys, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

[2] East Carolina Univ, Dept Math, Greenville, NC 27858 USA

[3] Univ Glasgow, Sch Math & Stat, Univ Pl, Glasgow G12 8QQ, Lanark, Scotland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 10期

关键词：

Numerical semigroups; C*-envelope; rigidity; K-THEORY; CROSSED-PRODUCTS; REPRESENTATIONS;

D O I：

10.1090/proc/15096

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A higher rank numerical semigroup is a positive cone whose seminormalization is isomorphic to the free abelian semigroup. The corresponding nonselfadjoint semigroup algebras are known to provide examples that answer Arveson's Dilation Problem in the negative. Here we show that these algebras share the polydisc as the character space in a canonical way. We subsequently use this feature in order to identify higher rank numerical semigroups from the corresponding nonselfadjoint algebras.

引用

页码：4423 / 4433

页数：11

共 50 条

[21] CONVERGENCE OF POSITIVE OPERATOR SEMIGROUPS
Gerlach, Moritz
Glueck, Jochen
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (09) : 6603 - 6627
[22] NUMERICAL SEMIGROUPS THAT ARE FRACTIONS OF NUMERICAL SEMIGROUPS OF MAXIMAL EMBEDDING DIMENSION
Smith, Harold J.
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2010, 17 (01): : 69 - 96
[23] TENSOR DECOMPOSITION, PARAFERMIONS, LEVEL-RANK DUALITY, AND RECIPROCITY LAW FOR VERTEX OPERATOR ALGEBRAS
Jiang, Cuipo
Lin, Zongzhu
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 375 (12) : 8325 - 8352
[24] LIMITS AND C*-ALGEBRAS OF LOW RANK OR DIMENSION
Brown, Lawrence G.
Pedersen, Gert K.
JOURNAL OF OPERATOR THEORY, 2009, 61 (02) : 381 - 417
[25] Representations of higher-rank graph C*-algebras associated to Λ-semibranching function systems
Farsi, Carla
Gillaspy, Elizabeth
Jorgensen, Palle
Kang, Sooran
Packer, Judith
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 468 (02) : 766 - 798
[26] C*-Algebras of Algebraic Dynamical Systems and Right LCM Semigroups
Brownlowe, Nathan
Larsen, Nadia S.
Stammeier, Nicolai
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2018, 67 (06) : 2453 - 2486
[27] Amalgams of Inverse Semigroups and C*-Algebras
Donsig, Allan P.
Haataja, Steven P.
Meakin, John C.
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2011, 60 (04) : 1059 - 1076
[28] Inverse semigroups and combinatorial C*-algebras
Exel, Ruy
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2008, 39 (02): : 191 - 313
[29] C*-algebras generated by cancellative semigroups
Grigoryan, S. A.
Salakhutdinov, A. F.
SIBERIAN MATHEMATICAL JOURNAL, 2010, 51 (01) : 12 - 19
[30] Inverse semigroups and combinatorial C*-algebras
Ruy Exel*
Bulletin of the Brazilian Mathematical Society, New Series, 2008, 39 : 191 - 313

← 1 2 3 4 5 →