A non-simply laced version for cluster structures on 2-Calabi-Yau categories

Details A non-simply laced version for cluster structures on 2-Calabi-Yau categories A non-simply laced version for cluster structures on 2-Calabi-Yau categories

2009-10-27

arxiv.org/abs/0910.5077v1

Mathematics

Representation Theory

27 pages

Scientific paper

We propose a non simply-laced version for cluster structures on additive Krull-Schmidt categories over arbitrary commutative base field. Starting from the work of Buan-Iyama-Reiten-Scott, it turns out that, under the same weaker assumption as in the simply-laced case, the generalized version of cluster structure holds for 2-Calabi-Yau or stably 2-Calabi-Yau categories. As a direct consequence, we can use the so-called cluster maps to realize in a direct way a large class of non simply-laced cluster algebras of geometric type with coefficients associated with rectangular matrices whose principal parts are skew symmetrizable.

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