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Yurii S. Samoilenko

Publications and source records attributed to Yurii S. Samoilenko.

4 recordsLinked to original sources
arXiv2006

On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles

For a class of $*$-algebras, where $*$-algebra $A_{Γ,τ}$ is generated by projections associated with vertices of graph $Γ$ and depends on a parameter $τ$ $(0 < τ\leq 1)$, we study the sets $Σ_Γ$ of values of $τ$ such that the algebras $A_{Γ,τ}$ have nontrivial $*$-representations, by using the theory of spectra of graphs. In other words, we study such values of $τ$ that the corresponding configurations of subspaces in a Hilbert space exist.

math.RT↗
arXiv2006

On Transitive Systems of Subspaces in a Hilbert Space

Methods of *-representations in Hilbert space are applied to study of systems of $n$ subspaces in a linear space. It is proved that the problem of description of $n$-transitive subspaces in a finite-dimensional linear space is *-wild for $n \geq 5$.

math.RT↗
arXiv2003

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.

math.OA↗