163 citations · 327 across the 36 of their papers we have counts for
10 papers · 1 filter
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…
Algebras of Quasi-Plücker Coordinates are Koszul
Robert Laugwitz, Vladimir Retakh
Motivated by the theory of quasi-determinants, we study non-commutative algebras of quasi-Plücker coordinates. We prove that these algebras provide new examples of non-homogeneous…
Noncommutative Cross-Ratios
Vladimir Retakh
We present a definition of and discuss basic properties of cross-ratios over noncommutative skew-fields. A new theorem was added.
Hilbert series of algebras associated to direct graphs and order homology
Vladimir Retakh, Shirlei Serconek, Robert Wilson
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necess…