Related papers: Virtual mutations of weighted surface algebras

Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and…

Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…

In this paper we study the structure of Gabriel quivers of tame symmetric algebras of period four. More precisely, we focus on algebras having Gabriel quiver {\it biregular}, i.e. the numbers of arrows starting and ending at any vertex are…

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular,…

Following methods used by A. Dugas for investigating derived equivalent pairs of (weakly) symmetric algebras, we apply them in a specific situation, obtaining new deep results concerning iterated mutations of symmetric periodic algebras.…

Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…

The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…

We classify all mutation-finite quivers with real weights. We show that every finite mutation class not originating from an integer skew-symmetrizable matrix has a geometric realization by reflections. We also explore the structure of…

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian…

We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on…

We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving mutations between fake weighted…

We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set…

The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…

We investigate commutative analogues of Clifford algebras -- algebras whose generators square to $\pm1$ but commute, instead of anti-commuting as they do in Clifford algebras. We observe that commutativity allows for elegant results. We…

We present a categorification of four mutation finite cluster algebras by the cluster category of the category of coherent sheaves over a weighted projective line of tubular weight type. Each of these cluster algebras which we call tubular…

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…

Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…

We introduce the notion of (nondegenerate) strong-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the modular group SL(2,Z) whose kernel contains a…

We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. For this, we introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group…

We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge),…