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