Finite Generation of Ext and (D,A)-stacked Algebras
Joanne Leader
2381/29029
https://figshare.le.ac.uk/articles/thesis/Finite_Generation_of_Ext_and_D_A_-stacked_Algebras/10140116
We 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.
2014-08-08 13:59:03
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