Related papers: Quivers with subadditive labelings: classification…

For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called…

We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…

We classify the twisted tensor products of a finite set algebra with a two elements set algebra using colored quivers obtained through considerations analogous to Ore extensions. This provides also a classification of entwining structures…

Let A be a finitely presented associative monomial algebra. We study the category qgr(A) which is a quotient of the category of graded finitely presented A-modules by the finite-dimensional ones. As this category plays a role of the…

One of the remarkable properties of cluster algebras is that any cluster, obtained from a sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the initial cluster (known as the "Laurent phenomenon").…

Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to quivers. As case of study, we investigate the consequences…

Important objects of study in $\tau$-tilting theory include the $\tau$-tilting pairs over an algebra on the form $kQ/I$, with $kQ$ being a path algebra and $I$ an admissible ideal. In this paper, we study aspects of the combinatorics of…

We extend Carter's notion of admissible diagrams and attach a "Dynkin-like" diagram to each reduced reflection factorization of an element in a finite Weyl group. We give a complete classification for the diagrams attached to reduced…

Transformers can perform in-context classification from a few labeled examples, yet the inference-time algorithm remains opaque. We study multi-class linear classification in the hard no-margin regime and make the computation identifiable…

We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…

We prove that in the varieties where every compact congruence is a factor congruence and every nontrivial algebra contains a minimal subalgebra, a finitely presented algebra is projective if and only if it has every minimal algebra as its…

We study quivers in the context of matrix models. We introduce chains of generalized Konishi anomalies to write the quadratic and cubic equations that constrain the resolvents of general affine and non-affine quiver gauge theories, and give…

To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is finite dimensional and gentle. We study the stability…

The theory of representations of quivers and of their preprojective algebras are reviewed. In particular, moduli spaces of representations of these algebras, quiver varieties and reflection functor are described. The proof that the…

For any acyclic quiver, we establish a family of structure isomorphisms for its cohomological Hall algebra (CoHA). The family is parameterized by partitions of the quiver into Dynkin subquivers. For each such partition, we write the domain…

We propose an alternative description of 2 dimensional Conformal Field Theory in terms of Quantum Inverse Scattering. It is based on the generalized KdV systems attached to $A_2^{(2)}$, yielding the classical limit of Virasoro as Poisson…

Combining results from Keller and Buchweitz, we describe the 1-periodic derived category of a finite dimensional algebra $A$ of finite global dimension as the stable category of maximal Cohen-Macaulay modules over some Gorenstein algebra…

The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, defining a Coxeter element and thereby a double Bruhat cell. We use…

We show that quadratic Hamiltonians in involution coming from a St\"ackel system are quantizable, in the sense that one can construct commutative self-adjoint operators whose symbols are the quadratic Hamiltonians. Moreover, they allow…

We study a discrete dynamic on weighted bipartite graphs on a torus, analogous to dimer integrable systems in Goncharov-Kenyon 2013. The dynamic on the graph is an urban renewal together with shrinking all 2-valent vertices, while it is a…