Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0708.4189

Some algorithms for semi-invariants of quivers

D. A. Shmelkin
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present some theorems and algorithms for calculating perpendicular categories and locally semi-simple decompositions. We implemented a computer program {\sc TETIVA} based on these algorithms and we offer this program for everybody's use.

Explore related subjects

math.RTmath.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

D. A. Shmelkin. 2007-08-30. Some algorithms for semi-invariants of quivers. https://arxiv.org/abs/0708.4189

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

KEEP EXPLORING

Related papers

arXiv2026

How to superize $\mathfrak{gl}(\infty)$

Penkov with co-authors studied several types of Lie algebra $\mathfrak{gl}(\infty)$. Completely different new types of super versions of $\mathfrak{gl}(\infty)$ are introduced in this paper: these are Lie superalgebras of supermatrices infinite in all directions with non-zero elements of each matrix occupying a region around the main diagonal bounded by certain curves, not straight lines. Several open questions related with further study of the Lie superalgebras introduced and with their possible applications to dynamical systems, such as KdV, are formulated.

math.RT↗
arXiv2026

Cochain complexes over an endofunctor

We introduce the categories of left and right complexes for (additive) endofunctors over an additive category $\mathcal{C}$. These categories unify the definitions of complexes over an additive category and modules over repetitive algebras. Supported by Eilenberg-Moore theory and Happel's successful work, we study the descriptions and properties of these categories, highlighting both similarities and differences with complexes and modules over repetitive algebras. We also examine the influence and interaction of these categories with the category of endofunctors, leading to applications in the representation theory of algebras and with eventual applications in ($2$-)algebraic geometry.

math.RT↗
arXiv2026

The double super Yangians in type A for arbitrary $0^m 1^n$-sequences and their bosonic representations

In this paper, we introduce the double super Yangian $\mathrm{DY}_{h}(\mathfrak{gl}_{m|n}^{\mathfrak{s}})$ and $\mathrm{DY}_{h}(\mathfrak{sl}_{m|n}^{\mathfrak{s}})$ associated with any fixed $0^{m}1^{n}$-sequence $\mathfrak{s}$. First, we establish an explicit isomorphism between the Drinfeld and R-matrix presentations of $\mathrm{DY}_{h}(\mathfrak{gl}^{\mathfrak{s}}_{m|n})$. We then generalize the notion of the quantum Berezinian to $\mathrm{DY}_{h}(\mathfrak{gl}_{m|n}^{\mathfrak{s}})$, and employ it to construct the R-matrix presentation of $\mathrm{DY}_{h}(\mathfrak{sl}_{m|n}^{\mathfrak{s}})$ and prove that it is isomorphic to the Drinfeld presentation. As an application, we present level-1 bosonic representations for $\mathrm{DY}_{h}(\mathfrak{gl}_{m|n}^{\mathfrak{s}})$ and $\mathrm{DY}_{h}(\mathfrak{sl}_{m|n}^{\mathfrak{s}})$ in terms of their Drinfeld current generators.

math.RT↗