Koszul Duality for Multigraded Algebras

Hawwa, F. T.; William Hoffman, J.; Wang, Haohao
October 2012
European Journal of Pure & Applied Mathematics;2012, Vol. 5 Issue 4, p511
Academic Journal
Classical Koszul duality sets up an adjoint pair of functors, establishing an equivalence F : Db(A) ⇆ Db(A!) : G, where A is a quadratic algebra, A! is the quadratic dual, and Db refers to the bounded derived category of complexes of graded modules over the graded algebra (i.e., A or A!). This duality can be extended in many ways. We consider here two extensions: first we wish to allow a ∧-graded algebra, where ∧ is any abelian group (not just Z). Second, we will allow filtered algebras. In fact we are considering filtered quadratic algebras with an (internal) ∧-grading.


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