Algebras of Finite Context Type

Cluster-tilted Algebras of Finite Representation Type

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 (basic) cluster-tilted algebra of finite type is uniquely determined by its quiver. Also some necessary conditions on the shapes of quivers of cluster-tilted a...

On Algebras of Finite Representation Type

Since D. G. Higman proved that bounded representation type and finite representation type are equivalent for group algebras at prime characteristic, there has been a renewed interest in the Brauer-Thrall conjecture that bounded representation type implies finite representation type for arbitrary algebras. The main purpose of this paper is to present a new approach to this conjecture by showing ...

Recognizing Cluster Algebras of Finite Type

Cluster algebras were introduced in [5] by Fomin and Zelevinsky to provide an algebraic framework for the study of canonical bases in quantum groups. Since their introduction, it has also been observed that cluster algebras are closely related with different areas in mathematics. For example; they provide a natural algebraic setup to study recursively defined rational functions in combinatorics...

Lie Algebras of Finite and Affine Type

Hecke Algebras of Finite Type Are Cellular

Let H be the one-parameter Hecke algebra associated to a finite Weyl group W , defined over a ground ring in which “bad” primes for W are invertible. Using the Kazhdan–Lusztig basis of H, we show that H has a natural cellular structure in the sense of Graham and Lehrer. Previously, this was only known in type An and Bn. Thus, we obtain a general theory of “Specht modules” for Hecke algebras of ...