The taylor resolution over a skew polynomial ring - with Frank Moore and Desiree Martin

Abstract: Let I be a monomial ideal in the polynomial ring R = k[x1, . . . , xn] over a field k. In her thesis, Taylor introduced a complex which provides a multi-graded free resolution for R/I as an R-module. Later, Gemeda provided a differential graded structure on this complex while Avramov showed that this DG algebra admits a divided power structure. We generalize these results to monomial ideals J in a skew polynomial ring S. As an application we show that if one fixes the number of generators of the ideal J, then there are finitely many isomorphism classes for π ≥2 (S/J), where π(S/J) is the homotopy color Lie algebra of S/J, an invariant which was introduced and studied by the first and last author in a different work. As a result it follows that there are finitely many possibilities for the Poincar´e series of k over S/J, if the number of generators of J is fixed.

commutative algebraalgebraic topologyquantum algebrarepresentation theory

Audience: researchers in the topic

DG methods in commutative algebra and representation theory

Series comments: Description: Online special session

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