4 citations · 5 across the 6 of their papers we have counts for
9 papers
On equivalence classes of homotopes of algebras and trilinear forms
Sergey Guminov, Ilya Zhdanovskiy
A homotope, or a mutation, of a -algebra is a new algebra with the same underlying space, but with the multiplication law dependent on the multiplication law of the original alg…
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…
On the structutre of the algebra generated by the non-commutative operator graph demonstrating superactivation for a zero-error capacity
Grigori G. Amosov, I. Yu. Zhdanovskiy
Recently M.E. Shirokov introduced the non-commutative operator graph depending on the complex parameter to construct channels with positive quantum zero-error capacity having v…
Orthogonal pairs and mutually unbiased bases
Alexey Bondal, Ilya Zhdanovskiy
The paper is devoted to representation theoretic and algebraic geometric aspects of the theory of orthogonal decompositions of Lie algebra sl(n) into Cartan subalgebras orthogonal…
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…
Coherence of relatively quasi-free algebras
Alexey Bondal, Ilya Zhdanovskiy
We prove coherence of relatively quasi-free algebras over noetherian rings. Chase criterion for coherence is used.