Explicit description of generic representations for quivers of type An or Dn

We describe explicitly a generic representation for Dynkin quivers of type An or Dn for any dimension vector.

Cluster algebras, quiver representations and triangulated categories

This is an introduction to some aspects of Fomin-Zelevinsky’s cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer schools held in 2006 (Bavaria)and 2008 (Jerusalem). In addition to by now classical material, we present the outline of a proof of the periodicity conjecture for pairs of Dynkin diagrams (details will appear elsewhere) and recent results on the interpretation of mutations as derived equivalences.

The bound quiver of a split extension

In this paper, we give a sufficient (which is also necessary under a compatibility hypothesis) condition on a set of arrows in the quiver of an algebra A so that A is a split extension of A/M, where M is the ideal of A generated by the classes of these arrows. We also compare the notion of split extension with that of semiconvex extension of algebras.

On moduli spaces for abelian categories

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories.

On the composite of irreducible morphisms in almost sectional paths

We study here when the composite of it irreducible morphisms in almost sectional paths is non-zero and lies in Rn+1 (C) 2007 Elsevier B.V. All rights reserved.

ON THE COMPOSITE OF THREE IRREDUCIBLE MORPHISMS IN THE FOURTH POWER OF THE RADICAL

We study here the nonzero composite of three irreducible morphisms between indecomposable modules lying in the fourth power of the radical.

Gaiotto duality for the twisted A(2N-1) series

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Class Notes for Math 918: Cohen Macaulay Modules, Instructor Roger Wiegand

Topics covered are: Cohen Macaulay modules, zero-dimensional rings, one-dimensional rings, hypersurfaces of finite Cohen-Macaulay type, complete and henselian rings, Krull-Remak-Schmidt, Canonical modules and duality, AR sequences and quivers, two-dimensional rings, ascent and descent of finite Cohen Macaulay type, bounded Cohen Macaulay type.

Good stories for great holidays, arranged for story-telling and reading aloud and for the children's own reading,

"Reference lists for story-telling and collateral reading": p. [429]-443.