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14 November 2008 at the Westfälische Wilhelms-Universität Münster
Abstracts
Marcel Wiedemann: Constructions with real root representations of quivers
Let Q be a quiver. V. Kac showed that the dimension vectors of
indecomposable representations correspond to the positive roots of the
associated Kac-Moody algebra. Moreover, there exists a unique indecomposable
representation corresponding to each positive real root, called a real root
representation. In this talk we shall discuss the following
question: "How can one 'construct' real root representations and what are
their 'properties'? We introduce the maximal rank type property for
representations of quivers and use this property of real root
representations to construct all real root representations of a certain
class of quivers using Universal Extension Functors, introduced by C.
Ringel. Moreover, we discuss examples of representations which cannot be
constructed using Universal Extension Functors.
Qunhua Liu
This is a joint work with L. Angeleri Hügel and S. Koenig. We investigate
the
relation between tilting modules of a ring and the recollement structures on
the derived module category. More precisely, on one hand, we construct a
recollement of the derived module category from a tilting module of
projective
dimension bounded by one. On the other hand, we construct a tilting object
from
a recollement which has two partital tilting objects satisfying some
Hom-vanishing condition.
Markus Perling: Exceptional Sequences of Invertible Sheaves on Rational Surfaces
In this talk we consider tilting sheaves on rational algebraic
surfaces which decompose into direct sums of invertible sheaves.
We present a structure theorem for such sheaves and give a
geometric criterion for their existence. We present a complete
classification for the case of toric surfaces.
Jeanne Scott: The affine GLS $\varphi$-map and 'chess' Kostka numbers
I will discuss how to compute the Geiss-Leclerc-Schr\"oer
$\varphi$-map for 'shape modules' over the affine prepro jective algebra
in terms of 'chess' Kostka numbers.
Sefi Ladkani: A linear algebra identity, its categorification, and the Coxeter
transformation
A linear algebra identity, which can be traced back to Bourbaki, states that
a certain product of pseudo-reflections, defined for any square matrix B,
can be expressed as B1*B2, where B1 and B2 are closely associated with the
upper and lower triangular parts of B. In particular this applies to the
Coxeter transformation corresponding to a generalized Cartan matrix.
A result of Gabriel asserts that for path algebras of trees, the
Auslander-Reiten translation is isomorphic to the Coxeter functor, defined
by Bernstein-Gelfand-Ponomarev as the product of their reflection functors.
In the talk I will explain the above results and why the latter can be
viewed as a categorification of the former. I will then present a new,
analogous result, based on a different construction, that yields a
categorification of wider scope over any finite dimensional triangular
algebra.
lutzhille@uni-muenster.de
Letzte Änderung: 20.10.2008
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