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Representation Dimension and Quasi-hereditary Algebras

✍ Scribed by Changchang Xi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
148 KB
Volume
168
Category
Article
ISSN
0001-8708

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✦ Synopsis

dedicated to professor idun reiten for her 60th birthday

We study Auslander's representation dimension of Artin algebras, which is by definition the minimal projective dimension of coherent functors on modules which are both generators and cogenerators. We show the following statements: (1) if an Artin algebra A is stably hereditary, then the representation dimension of A is at most 3. (2) If two Artin algebras are stably equivalent of Morita type, then they have the same representation dimension. Particularly, if two self-injective algebras are derived equivalent, then they have the same representation dimension. (3) Any incidence algebra of a finite partially ordered set over a field has finite representation dimension. Moreover, we use results on quasi-hereditary algebras to show that (4) the Auslander algebra of a Nakayama algebra has finite representation dimension.

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