2021/08/31 by Luigi Ferraro, Ferraro, Luigi, Desiree Martin +3
Mathematics · #16E05 #16E40 #16E45 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2109.00111
openalex publication_date 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \Bbbk be a field and let I be a monomial ideal in the polynomial ring Q=\Bbbk[x1,…,xn]. In her thesis, Taylor introduced a complex which provides a finite free resolution for Q/I as a Q-module. Later, Gemeda constructed a differential graded structure on the Taylor resolution. More recently, Avramov showed that this differential graded algebra admits divided powers. We generalize each of these results to monomial ideals in a skew polynomial ring R. Under the hypothesis that the skew commuting parameters defining R are roots of unity, we prove as an application that as I varies among all ideals generated by a fixed number of monomials of degree at least two in R, there is only a finite number of possibilities for the Poincaré series of \Bbbk over R/I and for the isomorphism classes of the homotopy Lie algebra of R/I in cohomological degree larger or equal to two.