On C*-algebras generated by pairs of q-commuting isometries

We consider the C*-algebras O_2^q and A_2^q generated, respectively, by isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 = complex conjugate of q_2. In the second part of our paper, we discuss the complexity of the representation theory of A_2^q. We show that A_2^q is *-wild for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treate

On q-tensor products of Cuntz algebras

We consider the C∗-algebra Eqn, m, which is a q-twist of two Cuntz-Toeplitz algebras. For the case |q| &lt; 1, we give an explicit formula which untwists the q-deformation showing that the isomorphism class of Eqn, mdoes not depend on q. For the case |q| = 1, we give an explicit description of all ideals in Eqn, m. In particular, we show that Eqn, mcontains a unique largest ideal Mq. We identify Eqn, m/Mq with the Rieffel deformation of On ⊗Om and use a K-theoretical argument to show that the isomorphism class does not depend on q. The latter result holds true in a more general setting of multiparameter deformations

Risk Management in Customs as a Factor in Ensuring Customs Security During the Economic Downturn

The article analyzes the fiscal significance of customs payments, namely: VAT, duties and excise tax, which are payed with customs clearance goods. It is defined that the role of budget revenues by these payments is extremely important. It is emphasized that the relevance of full and timely receipt of payments, which are accumulated by the State Customs Service of Ukraine, is especially increased during periods of economic downturn in the country, when the business activity of certain economic entities and sectors of the economy is significantly reduced. It is determined that the number and volume of offenses that are detected at the customs and can lead to significant budget losses are quite high and in recent periods tend to increase, which indicates the need to ensure effective customs control by the State and increase of the customs security. The publication specifies that the current global trend of customs control development, which is also typical for Ukraine, is the refusal of continuous control in favor of a selective one, with additional application of risk-oriented approach. The advantages of this approach to customs control are provided. The domestic experience of risk management in customs on the part of relevant authorities by using the Automated Risk Management System (ARMS) is analyzed. The need to constantly update and improve the algorithms of the ARMS and the system itself, as well as continuous updating of databases by adjusting, deleting and creating new risk profiles, is underlined. This is connected with the instability of the sphere of customs risks.</jats:p