Related papers: Special Biserial Cluster-tilted Algebras
Let $G=SL(2,5)$ be the special linear group of $2 \times 2$-matrices with coefficients in the field with $5$ elements. We show that the principal block over a splitting field $K$ of characteristic two of the group algebra $KG$ has a…
Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. We investigate the structure properties of the endomorphism algebras of semi-tilting $A$-modules, and prove that the endomorphism algebras arising from the…
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that there exists a bijection between the tilting…
A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…
We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in…
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
In this paper we treat the $\tau$-tilting finiteness of biserial (respectively special biserial) algebras over algebraically closed (respectively arbitrary) fields. Inside these families, to compare the notions of representation-finiteness…
Let $K$ be a differential field over $\C$ with derivation $D$, $G$ a finite linear automorphism group over $K$ which preserves $D$, and $K^G$ the fixed point subfield of $K$ under the action of $G$. We show that every finite-dimensional…
In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. Firstly, we give a complete list of symmetric algebras with radical cube zero…
We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.
This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.
We give a precise definition of folded quivers and folded cluster algebras. We give many examples of including some with finite mutation structure that do not have analogues in the unfolded cases. We relate these examples to the finite…
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
We describe a new way to relate an acyclic, skew-symmetrizable cluster algebra to the representation theory of a finite dimensional hereditary algebra. This approach is designed to explain the c-vectors of the cluster algebra. We obtain a…
Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose…
The notion of mutation plays crucial roles in representation theory of algebras. Two kinds of mutation are well-known: tilting/silting mutation and quiver-mutation. In this paper, we focus on tilting mutation for symmetric algebras.…
Superspecies are introduced to provide the nice constructions of all finite-dimensional superalgebras. All acyclic superspecies, or equivalently all finite-dimensional (gr-basic) gr-hereditary superalgebras, are classified according to…
We determine all two-dimensional Lie subalgebras of the centreless Virasoro algebra and complete the characterization of all finite dimensional Lie subalgebras of the complex Virasoro algebra.