163 citations · 327 across the 36 of their papers we have counts for
15 papers · 1 filter
Noncommutative Catalan numbers
Arkady Berenstein, Vladimir Retakh
The goal of this paper is to introduce and study noncommutative Catalan numbers which belong to the free Laurent polynomial algebra in generators. Our noncommutative numb…
Noncommutative marked surfaces
Arkady Berenstein, Vladimir Retakh
The aim of the paper is to attach a noncommutative cluster-like structure to each marked surface . This is a noncommutative algebra generated by "noncommutative…
Generalized adjoint actions
Arkady Berenstein, Vladimir Retakh
The aim of this paper is to generalize the classical formula by replacing with any formal power series $\displaysty…
A short proof of Kontsevich cluster conjecture
Arkady Berenstein, Vladimir Retakh
We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map K_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1}) are given by nonco…
Lie algebras and Lie groups over noncommutative rings
Arkady Berenstein, Vladimir Retakh
The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra sitting inside an associative algebra and any a…
Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs
Israel Gelfand, Sergei Gelfand, Vladimir Retakh +1
To directed graphs with unique sink and source we associate a noncommutative associative alsgebra and a polynomial over this algebra. Edges of the graph correspond to pseudo-roots…