Lusztig conjectures, old and new, I.
Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras
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...
Matrix factorizations for domestic triangle singularities
Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context,...
Matrix problems and Drozd's theorem
Matrix problems and stable homotopy types of polyhedra
This is a survey of the results on stable homotopy types of polyhedra of small dimensions, mainly obtained by H.-J. Baues and the author [3, 5, 6]. The proofs are based on the technique of matrix problems (bimodule categories).
Maximal Orders of global dimension and Krull dimension two.
Minimal algebras of infinite representation type with preprojective component.
Minimal bipartite algebras of infinite prinjective type with prin-preprojective component
Minimal Representation-Infinite Coil Algebras.
Minimal singularities for representations of Dynkin quivers.
Moduled categories and adjusted modules over traced rings [Book]
Modules and quiver representations whose orbit closures are hypersurfaces
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite-dimensional A-modules whose orbit closures are local hypersurfaces. The result is reduced to an analogous characterization for orbit closures of quiver representations obtained in Section 3.
Modules de type quasi fini sur un anneau non commutatif
Modules homogènes et anneaux localement homogènes
Modules of finite projective dimension and cocovers.
Modules quasi-projectifs, projectifs et parfaits
Modules tertiaires
Moduln über einreihigen Ringen.
More hammocks
Mutating seeds: types and .
In the cases and , we describe the seeds obtained by sequences of mutations from an initial seed. In the case, we deduce a linear representation of the group of mutations which contains as matrix entries all cluster variables obtained after an arbitrary sequence of mutations (this sequence is an element of the group). Nontransjective variables correspond to certain subgroups of finite index. A noncommutative rational series is constructed, which contains all this information.