163 citations · 287 across the 18 of their papers we have counts for
6 papers · 1 filter
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…
On a class of algebras associated to directed graphs
Israel Gelfand, Vladimir Retakh, Shirlei Serconek +1
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Suc…
Quaternionic quasideterminants and determinants
Israel Gelfand, Vladimir Retakh, Robert Lee Wilson
We compute quaisideterminants and determinants of quaternionic matrices
Hilbert series of quadratic algebras associated with pseudo-roots of noncommutative polynomials
Israel Gelfand, Sergei Gelfand, Vladimir Retakh +2
The quadratic algebras Q_n are associated with pseudo-roots of noncommutative polynomials. We compute the Hilbert series of the algebras Q_n and of the dual quadratic algebras Q_n^…
Noncommutative algebras associated to complexes and graphs
Israel Gelfand, Sergei Gelfand, Vladimir Retakh
This is a first of our papers devoted to "noncommutative topology and graph theory". Its origin is the paper math.QA/0002238 by I. Gelfand, V. Retakh, and R.L. Wilson where a new c…
Quadratic-linar algebras associated with factorizations of noncommutative polynomials and noncommutative differential polynomials
Israel Gelfand, Vladimir Retakh, Robert Lee Wilson
This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined…