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 Ext -category of nice sets of simple objects of maximal projective dimension n is a finite length Frobenius category.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
