On structure of homogenenous Wick ideals in Wick ∗*-algebras with braided coefficients

We study the structure of Wick homogenenous ideals of higher degrees in quadratic algebras allowing Wick ordering. We present a method how to construct a homogeneous Wick ideal $\mathcal{I}_{n+1}$ of degree $n+1$ out of a homogeneous Wick ideal $\mathcal{I}_n$ of degree $n$ so that $\mathcal{I}_{n+1}\subset\mathcal{I}_n$. We show that in some particular cases our procedure allows one to get a description of the largest homogeneous Wick ideals of higher degrees having generators of the largest quadratic Wick ideal only. Finally we study classes of $*$-representations of Wick version of CCR annihilating certain homogeneous Wick ideals of degree higher than $2$

Енергетична незалежність України як критерій енергетичної безпеки

Найвагомішими показниками енергетичної безпеки, які визначають її енергетичну незалежність, є: 1) частка власних джерел у балансі паливно-енергетичних ресурсів (ПЕР) держави; 2) рівень імпортної залежності за домінуючим ресурсом у загальному постачанні первинної енергії (ЗППЕ); 3) частка імпорту ПЕР з однієї країни у загальному обсязі його імпорту

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| < 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

Unbounded representations of qq-deformation of Cuntz algebra

We study a deformation of the Cuntz-Toeplitz $C^*$-algebra determined by the relations $a_i^*a_i=1+q a_ia_i^*, a_i^*a_j=0$. We define well-behaved unbounded *-representations of the *-algebra defined by relations above and classify all such irreducible representations up to unitary equivalence.Comment: 13 pages, Submitted to Lett. Math. Phy