Currently displaying 1 – 6 of 6

Showing per page

Order by Relevance | Title | Year of publication

Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras

Thomas BrüstleLutz Hille — 2000

Colloquium Mathematicae

Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent to mat...

Actions of parabolic subgroups in GL_n on unipotent normal subgroups and quasi-hereditary algebras

Thomas BrüstleLutz Hille — 2000

Colloquium Mathematicae

Let R be a parabolic subgroup in G L n . It acts on its unipotent radical R u and on any unipotent normal subgroup U via conjugation. Let Λ be the path algebra k t of a directed Dynkin quiver of type with t vertices and B a subbimodule of the radical of Λ viewed as a Λ-bimodule. Each parabolic subgroup R is the group of automorphisms of an algebra Λ(d), which is Morita equivalent to Λ. The action of R on U can be described using matrices over the bimodule B. The advantage of this description is that each...

The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra

Lutz HilleDieter Vossieck — 2003

Colloquium Mathematicae

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.

Tilting Bundles on Rational Surfaces and Quasi-Hereditary Algebras

Lutz HilleMarkus Perling — 2014

Annales de l’institut Fourier

Let X be any rational surface. We construct a tilting bundle T on X . Moreover, we can choose T in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on X is equivalent to the bounded derived category of finitely generated modules over a finite dimensional quasi-hereditary algebra A . The construction starts with a full exceptional sequence of line bundles on X and uses universal extensions. If X is any smooth projective variety...

Page 1

Download Results (CSV)