Biserial algebras via subalgebras and the path algebra of D_4

Details Biserial algebras via subalgebras and the path algebra of D_4 Biserial algebras via subalgebras and the path algebra of D_4

2010-04-22

arxiv.org/abs/1004.3943v1

Mathematics

Representation Theory

Scientific paper

10.1016/j.jalgebra.2010.12.012

We give two new criteria for a basic algebra to be biserial. The first one states that an algebra is biserial iff all subalgebras of the form eAe where e is supported by at most 4 vertices are biserial. The second one gives some condition on modules that must not exist for a biserial algebra. These modules have properties similar to the module with dimension vector (1,1,1,1) for the path algebra of the quiver D_4. Both criteria generalize criteria for an algebra to be Nakayama. They rely on the description of a basic biserial algebra in terms of quiver and relations given by R. Vila-Freyer and W. Crawley- Boevey.

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