DMS Algebra Seminar

Speaker: Frank Moore (Wake Forest University)

Title: Color DG Algebra Techniques over Skew-Commutative Rings

Abstract: Differential graded (DG) algebra techniques in commutative algebra were introduced by Cartan, Eilenberg, and MacLane to compute the homology of Eilenberg-MacLane spaces. Since then, they have been used to great effect by Avramov, Gulliksen, Quillen, Roos, and many others to provide algebraic characterizations of rings with extremal homological behavior. We show that much of the foundations of this theory may be extended to quotients of skew-polynomial rings by normal elements, provided one works with so-called color DG algebras. We will discuss features of several joint works, coauthored with Luigi Ferraro, Desiree Martin, and Josh Pollitz.