Raquel
Coelho Simoes, Lancaster University
Simple-mindedness in negative Calabi-Yau cluster categories of
the hereditary type
Simple-minded systems were introduced by Koenig-Liu as
an abstraction of non-projective simple modules in stable module
categories. In this talk, we will consider simple-minded systems
in certain orbit categories of the bounded derived category of a
hereditary algebra, which can be considered to be negative
Calabi-Yau cluster categories. Simple-minded systems in this
setting turn out to play the role of cluster-tilting objects in
the positive Calabi-Yau setup. We will give a bijection between
simple-minded systems, simple-minded collections in the
fundamental domain and positive (higher) noncrossing partitions.
These results generalise the results of Iyama-Jin for Dynkin
type. This is based on joint work with David Pauksztello and
David Ploog.