5 papers
Theory of homotopes in application to mutually unbiased bases, harmonic analysis on graphs and perverse sheaves
Alexey Bondal, Ilya Zhdanovskiy
The paper is the survey of the modern results and applications of the theory of homotopes. The notion of a well-tempered element in an associative algebra is introduced and it is p…
Homotopes of finite-dimensional algebras
Ilya Zhdanovskiy
In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theo…
Partial abelianization of free product of algebras
Anna Kocherova, Ilya Zhdanovskiy
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algeb…
On the noncommutative deformation of the operator graph corresponding to the Klein group
G. G. Amosov, I. Yu. Zhdanovskiy
We study the noncommutative operator graph depending on complex parameter recently introduced by M.E. Shirokov to construct channels with positive quantum ze…
Symplectic geometry of unbiasedness and critical points of a potential
Alexey Bondal, Ilya Zhdanovskiy
The goal of these notes is to show that the classification problem of algebraically unbiased system of projectors has an interpretation in symplectic geometry. This leads us to a d…