Artin-Schelter regular algebras and categories |
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Authors: | Roberto Martiné z-Villa |
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Affiliation: | a Instituto de Matemáticas, Universidad Nacional Autonoma de Mexico, Campus Morelia, Apartado Postal 27-3 (Xangari), C.P. 58089, Morelia, Michoacán, Mexicob Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway |
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Abstract: | Motivated by constructions in the representation theory of finite dimensional algebras we generalize the notion of Artin-Schelter regular algebras of dimension n to algebras and categories to include Auslander algebras and a graded analogue for infinite representation type. A generalized Artin-Schelter regular algebra or a category of dimension n is shown to have common properties with the classical Artin-Schelter regular algebras. In particular, when they admit a duality, then they satisfy Serre duality formulas and the -category of nice sets of simple objects of maximal projective dimension n is a finite length Frobenius category. |
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Keywords: | Primary, 16P40, 16S38, 16E65, 18E05, 18A25, 18G20 Secondary, 16P90 |
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