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Dionne, Julie; Smith, David

Articulations of algebras and their homological properties. (English) Zbl 1150.16017

J. Algebra Appl. 5, No. 3, 345-359 (2006).
Summary: We give a construction of algebras, called articulation, which is a specific gluing of two non-simple algebras. Then, we describe the Auslander-Reiten theory of an algebra obtained in this way. This allows us to characterize the articulated algebras which are laura, left (or right) glued, weakly shod, shod, quasi-tilted or tilted.

Cited in 2 Documents

MSC:

16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras

Keywords:

articulated algebras; Auslander-Reiten quivers; laura algebras; finite-dimensional algebras; gluing non-simple algebras; weakly shod algebras; quasi-tilted algebras
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References:

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