The multisegment duality and the preprojective algebras of type .
The number of complete exceptional sequences for a Dynkin algebra
The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Δ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.
The number of elements in the mutation class of a quiver of type .
The p. p. ring and the Pierce sheaf representation of non-commutative rings
The periodicity conjecture for blocks of group algebras
We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.
The pure-projective ideal of a module category
The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
The Rational Invariants of the Tame Quivers.
The representation dimension of domestic weakly symmetric algebras
Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras...
The representation theory and the branching graph for the family of Turaev algebras .
The representation theory of the Temperley-Lieb algebras.
The spectral radius of the Coxeter transformations for a generalized Cartan matrix.
The standard form of a representation-finite algebra
The structure of primary modules
The structures of Hopf -algebra on Radford algebras
We investigate the structures of Hopf -algebra on the Radford algebras over . All the -structures on are explicitly given. Moreover, these Hopf -algebra structures are classified up to equivalence.
The vanishing of self-extensions over n-symmetric algebras of quasitilted type
A ring Λ satisfies the Generalized Auslander-Reiten Condition ( ) if for each Λ-module M with for all i > n the projective dimension of M is at most n. We prove that this condition is satisfied by all n-symmetric algebras of quasitilted type.
The Yoneda algebras of serial QF-algebras.
The Ziegler spectrum of a tame hereditary algebra
Tilting Bundles on Rational Surfaces and Quasi-Hereditary Algebras
Let be any rational surface. We construct a tilting bundle on . Moreover, we can choose in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on is equivalent to the bounded derived category of finitely generated modules over a finite dimensional quasi-hereditary algebra . The construction starts with a full exceptional sequence of line bundles on and uses universal extensions. If is any smooth projective variety...
Tilting Modules of Finite Projective Dimension.