Colloquium February 23
Date: Friday February 23
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Dieter Happel of Technische Uni Chemnitz
Title: Combinatorial aspects of tilting theory
Abstract
Quivers (i.e. directed graphs) and their representations have played a
decisive role in modern representation theory. Especially the Theorem
of Gabriel describing those quivers which admit only finitely many
indecomposable representations (up to isomorphism) was an important
step. The result says that the underlying graphs are the Dynkin diagrams
which occur in the classification of semisimple Lie algebras. Tilting
theory has been used in the past to transfer information from representations
of quivers to more general algebras and their modules. I will however
indicate in this talk a different aspect of tilting theory, namely how
tilting representations can be used to describe the internal structure
of the representations. For this we will associate with a quiver a
partially ordered set of tilting representations and first determine
explicitly the Hasse quiver (quiver of minimal inclusions) of this
poset. In a second step we will see what information is carried by this
Hasse quiver. Certain graph theoretic invariants yield already a lot of
information about the quiver we started with. A more detailed analysis
which only will be stated allows to reconstruct the quiver, if we assume
that the quiver was connected.
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