Related papers: Hall polynomials for representation-finite cluster…
We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences of the existence of Hall polynomials, in particular, we are…
We compute the Hochschild cohomology groups of the cluster-tilted algebras of finite representation type.
We use the comultiplication to prove that Hall polynomials exist for all finite and affine quivers. In the finite and cyclic cases, this approach provides a new and simple proof of the existence of Hall polynomials. In general, these…
We prove the existence of Hall polynomials for $x^2$-bounded invariant subspaces of nilpotent linear operators.
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
Let B be a cluster-tilted algebra. We prove that B is $\tau$-tilting finite if and only if B is representation-finite.
We show how a cluster-tilted algebra of finite representation type is related to the corresponding tilted algebra, in the case of algebras defined over an algebraically closed field.
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 are going to determine all the self-injective cluster tilted algebras. All are of finite representation type and special biserial.
Certain computable polynomials are described whose leading coefficients are equal to multiplicities in the tensor product decomposition for representations of a Lie algebra of ADE type.
We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation…
We present new classes of permutation polynomials over finite fields.
Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be recovered from the data of the corresponding…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
In the present paper we prove that Hall polynomial exists for each triple of decomposition sequences which parameterize isomorphism classes of coherent sheaves of a domestic weighted projective line $\mathbb X$ over finite fields. These…
An observation on Hall-Littlewood polynomials.
In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.
A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.
It is well known that the relation-extensions of tilted algebras are cluster-tilted algebras. In this paper, we extend the result to silted algebras and prove some extension of silted algebras are cluster-tilted algebras.
In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell…