163 citations · 327 across the 36 of their papers we have counts for
39 papers
Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries
Arkady Berenstein, Min Huang, Vladimir Retakh
The aim of the paper is to define noncommutative cluster structure on several algebras related to marked surfaces possibly with orbifold points of various orders, wh…
A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions
Irina Bobrova, Vladimir Retakh, Vladimir Rubtsov +1
We study a fully noncommutative generalisation of the commutative fourth Painlevé equation that possesses solutions in terms of an infinite Toda system over an associative unital d…
Symplectic groups over noncommutative algebras
Daniele Alessandrini, Arkady Berenstein, Vladimir Retakh +2
We introduce the symplectic group over a noncommutative algebra with an anti-involution . We realize several classical Lie groups as ove…
On the rational relationships among pseudo-roots of a non-commutative polynomial
Vladimir Retakh, Michael Saks
For a non-commutative ring R, we consider factorizations of polynomials in R[t] where t is a central variable. A pseudo-root of a polynomial p(t) is an element x in R, for which th…
Noncommutative cross-ratio and Schwarz derivative
Vladimir Retakh, Vladimir Rubtsov, Georgy Sharygin
We present here a theory of noncommutative cross-ratio, Schwarz derivative and their connections and relations to the operator cross-ratio. We apply the theory to "noncommutative e…
Noncommutative Shifted Symmetric Functions
Robert Laugwitz, Vladimir Retakh
We introduce a ring of noncommutative shifted symmetric functions based on an integer-indexed sequence of shift parameters. Using generating series and quasideterminants, this mult…