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Representation theory of algebras stably equivalent to an hereditary Artin algebra


Author: María Inés Platzeck
Journal: Trans. Amer. Math. Soc. 238 (1978), 89-128
MSC: Primary 16A64; Secondary 16A46
MathSciNet review: 0480635
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Abstract: Two artin algebras are stably equivalent if their categories of finitely generated modules modulo projectives are equivalent. The author studies the representation theory of algebras stably equivalent to hereditary algebras, using the notions of almost split sequences and irreducible morphisms. This gives a new unified approach to the theories developed for hereditary and radical square zero algebras by Gabriel, Gelfand, Bernstein, Ponomarev, Dlab, Ringel and Müller, as well as other algebras not covered previously. The techniques are purely module theoretical and do not depend on representations of diagrams. They are similar to those used by M. Auslander and the author to study hereditary algebras.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0480635-3
Article copyright: © Copyright 1978 American Mathematical Society