A Criterion for global dimension two for strongly simply connected schurian algebras

Details A Criterion for global dimension two for strongly simply connected schurian algebras A Criterion for global dimension two for strongly simply connected schurian algebras

2011-10-27

arxiv.org/abs/1110.6160v1

Mathematics

Rings and Algebras

18 pages, 19 figures

Scientific paper

The aim of this paper is to provide a criterion to determine, by quivers with relations, when an algebra has global dimension at most two. In order to do that, we introduce a new class of algebras of global dimension three, and we call them critical algebras. Furthermore we give a characterization of critical algebras by quivers with relations. Our main theorem states that if a strongly simply connected schurian algebra does not contain a critical algebra as a full subcategory, then it has global dimension at most two.

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