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It is well known that the Auslander algebra of any representation finite algebra is quasi-hereditary. We consider the Auslander algebra An of k[T]/〈n〉 (here, k is a field, T a variable and n a… (More)

We study the projective dimension of finitely generated modules over cluster-tilted algebras End𝒞(T) where T is a cluster-tilting object in a cluster category 𝒞. It is well-known that all… (More)

- Thomas Brüstle, Lutz Hille
- 2000

- Thomas Brüstle, Yu Qiu
- 2015

We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface $$\mathbf {S}$$S with marked points and non-empty boundary,… (More)

Acyclic cluster algebras have an interpretation in terms of tilting objects in a Calabi-Yau category defined by some hereditary algebra. For a given quiver Q it is thus desirable to decide if the… (More)

- Thomas Brüstle, Yang Han
- 2001

We determine the representation type of the algebras whose quiver has precisely two vertices and admits no loops by listing all minimal wild algebras of this form. It turns out that such an algebra A… (More)

Abstract We solve a long standing problem concerning the connection between the tameness of simply connected algebras and the weak nonnegativity of the associated Tits integral quadratic forms, and… (More)

We study the module category of a certain Galois covering of a cluster-tilted algebra which we call the cluster repetitive algebra. Our main result compares the module categories of the cluster… (More)

Abstract We give a criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of… (More)

- Thomas Brüstle, Lutz Hille
- 2000

Let P be a parabolic subgroup of some general linear group GL(V) where V is a finite-dimensional vector space over an infinite field. The group P acts by conjugation on its unipotent radical Pu and… (More)