Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0509260

Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs

Israel Gelfand·Sergei Gelfand·Vladimir Retakh·Robert Lee Wilson
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 of the polynomial. We give a sufficient condition when coefficients of the polynomial can be rationally expressed via elements of a given set of pseudo-roots (edges). Our results are based on a new theorem for directed graphs also proved in this paper.

Explore related subjects

math.QAmath.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Israel Gelfand, Sergei Gelfand, Vladimir Retakh, Robert Lee Wilson. 2005-09-12. Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs. https://doi.org/10.1007/s11005-005-0024-8

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Categorification of quasi-split iquantum groups

We introduce a new family of graded 2-categories generalizing the 2-quantum groups introduced by Khovanov, Lauda and Rouquier. We use them to categorify quasi-split iquantum groups in all symmetric types.

math.QA↗
arXiv2026

The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid

In a previous article, we showed that local projectivity is a sufficient condition for the existence of a bialgebroid structure on the ring of differential operators on an affine variety. In this note, we show using elementary methods that the ring of differential operators on a nodal curve is neither locally projective nor does it admit a bialgebroid structure.

math.QA↗
arXiv2026

Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction

We give complete conjugacy classes of modular group SL(2,Z). Particularly, the conjugacy classes of hyperbolic elements are decided by the proper equivalence classes of indefinite forms, and we give an example. Finally, we describe the coset representatives of centralizer of S, ST, T and hyperbolic elements of SL(2,Z) by regular continued fraction. In conclusion, most Nichols algebras over modular group are infinite-dimensional except Proposition 4.10.

math.QA↗