ON GORENSTEINNESS OF HOPF MODULE ALGEBRAS. (10th June 2016)

• Record Type: Journal Article
• Authors: SKRYABIN, SERGE
• Is Part Of: Glasgow mathematical journal. Volume 59:Part 2(2017)
• Page Start: 299
• Page End: 321
• Publication Date: 2016-06-10
• Subjects: 16T05; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0017089516000185
• Languages: English
• ISSNs: 0017-0895

Abstract

Abstract: Let H be a Hopf algebra with a bijective antipode, A an H -simple H -module algebra finitely generated as an algebra over the ground field and module-finite over its centre. The main result states that A has finite injective dimension and is, moreover, Artin–Schelter Gorenstein under the additional assumption that each H -orbit in the space of maximal ideals of A is dense with respect to the Zariski topology. Further conclusions are derived in the cases when the maximal spectrum of A is a single H -orbit or contains an open dense H -orbit.