Affine transformation crossed product type algebras and noncommutative surfaces

2009 ◽  
pp. 1-25 ◽  
Author(s):  
Joakim Arnlind ◽  
Sergei Silvestrov
Keyword(s):  
Affine Transformation ◽  
Product Type ◽  
Crossed Product

Spectra for Infinite Tensor Product Type Actions of Compact Groups

1996 ◽  
Vol 48 (2) ◽  
pp. 330-342
Author(s):  
Elliot C. Gootman ◽  
Aldo J. Lazar
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Abelian Groups ◽  
Product Type ◽  
Crossed Product ◽  
Compact Groups ◽  
Ideal Structure ◽  
Crossed Product Algebra ◽  
Product Algebra ◽  
The Ideal

AbstractWe present explicit calculations of the Arveson spectrum, the strong Arveson spectrum, the Connes spectrum, and the strong Connes spectrum, for an infinite tensor product type action of a compact group. Using these calculations and earlier results (of the authors and C. Peligrad) relating the various spectra to the ideal structure of the crossed product algebra, we prove that the topology of G influences the ideal structure of the crossed product algebra, in the following sense: if G contains a nontrivial connected group as a direct summand, then the crossed product algebra may be prime, but it is never simple; while if G is discrete, the crossed product algebra is simple if and only if it is prime. These results extend to compact groups analogous results of Bratteli for abelian groups. In addition, we exhibit a class of examples illustrating that for compact groups, unlike the case for abelian groups, the Connes spectrum and strong Connes spectrum need not be stable.

GENERALISED ARMENDARIZ PROPERTIES OF CROSSED PRODUCT TYPE

2015 ◽  
Vol 58 (2) ◽  
pp. 313-323
Author(s):  
LIANG ZHAO ◽  
YIQIANG ZHOU
Keyword(s):  
Semiprime Ring ◽  
Product Type ◽  
Crossed Product ◽  
Rigid Ring ◽  
Ordered Monoid ◽  
Armendariz Rings ◽  
Totally Ordered Monoid

AbstractLet R be a ring and M a monoid with twisting f:M × M → U(R) and action ω: M→ Aut(R). We introduce and study the concepts of CM-Armendariz and CM-quasi-Armendariz rings to generalise various Armendariz and quasi-Armendariz properties of rings by working on the context of the crossed product R*M over R. The following results are proved: (1) If M is a u.p.-monoid, then any M-rigid ring R is CM-Armendariz; (2) if I is a reduced ideal of an M-compatible ring R with M a strictly totally ordered monoid, then R/I being CM-Armendariz implies that R is CM-Armendariz; (3) if M is a u.p.-monoid and R is a semiprime ring, then R is CM-quasi-Armendariz. These results generalise and unify many known results on this subject.

The Standard Metric

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Affine Transformation ◽  
Convex Sets ◽  
Finite Dimension ◽  
Affine Subspace ◽  
Affine Transformations ◽  
Real Vector ◽  
Euclidean Metric ◽  
Affine Hyperplane ◽  
Tits Building ◽  
Convex Closure

This chapter presents some results about groups generated by reflections and the standard metric on a Bruhat-Tits building. It begins with definitions relating to an affine subspace, an affine hyperplane, an affine span, an affine map, and an affine transformation. It then considers a notation stating that the convex closure of a subset a of X is the intersection of all convex sets containing a and another notation that denotes by AGL(X) the group of all affine transformations of X and by Trans(X) the set of all translations of X. It also describes Euclidean spaces and assumes that the real vector space X is of finite dimension n and that d is a Euclidean metric on X. Finally, it discusses Euclidean representations and the standard metric.

scholarly journals On three-variable expanders over finite valuation rings

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Le Quang Ham ◽  
Nguyen Van The ◽  
Phuc D. Tran ◽  
Le Anh Vinh
Keyword(s):  
Valuation Ring ◽  
Product Type ◽  
Quadratic Polynomial ◽  
Valuation Rings

AbstractLet {\mathcal{R}} be a finite valuation ring of order {q^{r}}. In this paper, we prove that for any quadratic polynomial {f(x,y,z)\in\mathcal{R}[x,y,z]} that is of the form {axy+R(x)+S(y)+T(z)} for some one-variable polynomials {R,S,T}, we have|f(A,B,C)|\gg\min\biggl{\{}q^{r},\frac{|A||B||C|}{q^{2r-1}}\bigg{\}}for any {A,B,C\subset\mathcal{R}}. We also study the sum-product type problems over finite valuation ring {\mathcal{R}}. More precisely, we show that for any {A\subset\mathcal{R}} with {|A|\gg q^{r-\frac{1}{3}}} then {\max\{|AA|,|A^{d}+A^{d}|\}}, {\max\{|A+A|,|A^{2}+A^{2}|\}}, {\max\{|A-A|,|AA+AA|\}\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}}, and {|f(A)+A|\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}} for any one variable quadratic polynomial f.

scholarly journals Donation or Discount: Effect of Promotion Mode on Green Consumption Behavior

2021 ◽  
Vol 18 (4) ◽  
pp. 1912
Author(s):  
Jun Zou ◽  
Yifan Tang ◽  
Ping Qing ◽  
Han Li ◽  
Amar Razzaq
Keyword(s):  
Purchase Intention ◽  
Environmental Issues ◽  
Environmental Problems ◽  
Product Type ◽  
Mediation Effect ◽  
Green Consumption ◽  
Consumption Behavior ◽  
Conceptual Fluency ◽  
Global Concern ◽  
Practical Implications

Environmental issues are still challenging and of global concern. To improve the environmental consumption behavior of consumers, this study investigates whether the match between the promotion mode and product type can improve the conceptual fluency of consumers, so as to increase their purchase intention for green products. The results of three experiments reveal that the interaction between promotion mode and product type has a certain impact on the conceptual fluency of consumers, which can, in turn, promote their purchase intention. This research theoretically contributes to the research on green consumption by introducing promotion mode and revealing the mediation effect of conceptual fluency, it also provides some practical implications for alleviating environmental problems.

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