5 citations · 5 across the 4 of their papers we have counts for
8 papers · 1 filter
On a class of Koszul algebras associated to directed graphs
Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson
In math.QA/0506507 I. Gelfand and the authors introduced and studied a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for…
Noncommutative Double Bruhat cells and their factorizations
Arkady Berenstein, Vladimir Retakh
In the present paper we study noncommutative double Bruhat cells. Our main results are explicit positive matrix factorizations in the cells via quasiminors of matrices with noncomm…
Quasideterminants and Casimir elements for the general Lie superalgebra
Alexander Molev, Vladimir Retakh
We apply the techniques of quasideterminants to construct new families of Casimir elements for the general Lie superalgebra whose images under the Harish-Chandra isomorphism are re…
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…