Related papers: Quivers for silting mutation
We prove a conjecture of Nakajima (for type A the result was announced by Ginzburg- Vasserot) giving a geometric realization, via quiver varieties, of the Yangian of type ADE (and more in general of the Yangian associated to every symmetric…
We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potential (QPs) and mutations. The result also implies that…
We develop silting theory of a noetherian algebra $\Lambda$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $\Lambda$, and as a consequence, we see that mutation exists. As in the case of…
We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…
A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop, we introduce a quantity called a partition q-series. The partition q-series are…
In this paper, we give a complete classification of silted algebras for the quiver $\overrightarrow{\mathbb{A}}_{n}$ of type $\mathbb{A}_{n}$ with linear orientation and for the quiver obtained from $\overrightarrow{\mathbb{A}}_{n}$ by…
We give a precise definition of mutation of skew symmetrizable matrices over group rings and relate it to folding and mutation of quivers with symmetries. These matrices can have non-zero diagonal entries and we explain a mutation rule in…
To a quiver with involution, we show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the quantized Coulomb branch algebra of the 3d $\mathcal{N}=4$ involution-fixed part of the quiver gauge theory in…
We give a reduction technique for silting intervals in extriangulated categories, which we call "silting interval reduction". It provides a reduction technique for tilting subcategories when the extriangulated categories are exact…
We realize the enveloping algebra of the positive part of a semisimple complex Lie algebra as a convolution algebra of constructible functions on module varieties of some Iwanaga-Gorenstein algebras of dimension 1.
The main conjectures in Iwasawa theory predict the relationship between the Iwasawa modules and the $p$-adic $L$-functions. Using a certain proved formulation of the main conjecture, Greither and Kurihara described explicitly the (initial)…
Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…
We propose a mutation formula for the general rank from a principal component ${\rm PC}(\delta)$ of representations to another one ${\rm PC}(\epsilon)$ for a quiver with potential. We give sufficient conditions for the formula to hold. In…
Quiver mutation plays a crucial role in the definition of cluster algebras by Fomin and Zelevinsky. It induces an equivalence relation on the set of all quivers without loops and two-cycles. A quiver is called mutation-acyclic if it is…
The problem of solving non-linear equations would be considerably simplified by a possibility to convert known solutions into the new ones. This could seem an element of art, but in the context of ADHM-like equations describing quiver…
We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed…
A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into polygons and the bounded derived category of the gentle algebra has a geometric interpretation in terms of this surface. In this paper we study…
For finite-dimensional algebras over a field, Koenig and Yang established a bijection between silting complexes and simple-minded collections in the bounded derived category, with further contributions by many authors in various settings.…
We establish a connection between a generalization of KLR algebras, called quiver Schur algebras, and the cohomological Hall algebras of Kontsevich and Soibelman. More specifically, we realize quiver Schur algebras as algebras of…
We introduce a notion of mutation for $\tau$-exceptional sequences of modules over arbitrary finite dimensional algebras. For hereditary algebras, we show that this coincides with the classical mutation of exceptional sequences. For rank…