2014leaderjmphd.pdf (713.72 kB)
Finite Generation of Ext and (D,A)-stacked Algebras
thesis
posted on 2014-08-08, 13:59 authored by Joanne LeaderWe introduce the class of (D,A)-stacked algebras, which generalise the
classes of Koszul algebras, d-Koszul algebras and (D,A)-stacked monomial algebras.
We show that the Ext algebra of a (D,A)-stacked algebra is finitely generated in
degrees 0, 1, 2 and 3. After investigating some general properties of E(Ʌ) for this class
of algebras, we look at a regrading of E(Ʌ) and give examples for which the regraded
Ext algebra is a Koszul algebra. Following this we give a general construction of a
(D,A)-stacked algebra ~Ʌ from a d-Koszul algebra Ʌ, setting D = dA, with A ≥ 1.
From this construction we relate the homological properties of ~Ʌ and Ʌ, including
the projective resolutions and the structure of the Ext algebra.
History
Supervisor(s)
Cumming, Nicole; Petrovskiy, SergeiDate of award
2014-08-01Author affiliation
Department of MathematicsAwarding institution
University of LeicesterQualification level
- Doctoral
Qualification name
- PhD