Related papers: Quasi-cluster algebras from non-orientable surface…
The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular,…
The algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the $q$-bracket, is a quasimodular form. More generally, if a graded algebra $A$ of functions on…
Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized…
The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type $A_n$, by counting the mutation class of any quiver with underlying graph $A_n$. It will also follow that if $T$ and…
We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal…
In this paper we study multiserial and special multiserial algebras. These algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type. We define a module to be multiserial if its…
Suppose $l,m$ are natural numbers with $l\le m$, and $\mathbb{F}$ a field of characteristic $p$, and let $\mathcal{C}_{l,m}^{\mathbb{F}}$ denote the centraliser of the group algebra $\mathbb{F}S_l$ inside $\mathbb{F}S_m$. Ellers and Murray…
In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain all of the important homological and homotopical…
Let S be a commutative ring, Q a group that acts on S, and let R be the subring of S fixed under Q. A Q-normal S-algebra consists of a central S-algebra A and a homomorphism s from Q to the group Out(A) of outer automorphisms of A that…
In this paper, we compute the dimension of the Hochschild cohomology groups of any $m$-cluster tilted algebra of type $\tilde{\mathbb{A}}$. Moreover, we give conditions on the bounded quiver of an $m$-cluster tilted algebra $\Lambda$ of…
We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…
We relate commutative algebras in braided tensor categories to braid-reversed tensor equivalences, motivated by vertex algebra representation theory. First, for $\mathcal{C}$ a braided tensor category, we give a detailed construction of the…
We call a finite dimensional algebra A S-connected if the projective dimensions of the simple A-modules form an interval. We prove that a Nakayama algebra A is S-connected if and only if A is quasi-hereditary. We apply this result to…
Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…
We continue our investigation on cluster algebras arising from cluster tubes. Let $\mathcal{C}$ be a cluster tube of rank $n+1$. For an arbitrary basic maximal rigid object $T$ of $\mathcal{C}$, one may associate a skew-symmetrizable…
We extend the construction of canonical bases for cluster algebras from unpunctured surfaces to the case where the number of marked points is one, and we show that the cluster algebra is equal to the upper cluster algebra in this case.
We study maximal $m$-rigid objects in the $m$-cluster category $\mathcal C_H^m$ associated with a finite dimensional hereditary algebra $H$ with $n$ nonisomorphic simple modules. We show that all maximal $m$-rigid objects in these…
We study a commuting family of elements of the walled Brauer algebra $B_{r,s}(\delta)$, called the Jucys-Murphy elements, and show that the supersymmetric polynomials in these elements belong to the center of the walled Brauer algebra. When…
This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is…
This paper explores the cluster algebra structure of the moduli space $\mathscr{A}_{\mathrm{SL}_{n+1},\mathbb{S}}$ of twisted $\mathrm{SL}_{n+1}$-local systems on a surface. We derive general recurrence relations for cluster variables…