Cluster tilting and complexity

Details Cluster tilting and complexity Cluster tilting and complexity

2010-01-05

arxiv.org/abs/1001.0758v1

Mathematics

Category Theory

11 pages

Scientific paper

We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the underlying hereditary algebra. In the the second result, we study the bounded derived category of a cluster tilted algebra, and show that the maximal complexity occurring is either zero or one whenever the algebra is of finite or tame type.

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