4 papers
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…
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^…
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…