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Finite generation of some cohomology rings via twisted tensor product and Anick resolutions
Authors:Van C Nguyen  Xingting Wang  Sarah Witherspoon
Institution:1. Department of Mathematics, Hood College, Frederick, MD 21701, United States;2. Department of Mathematics, Temple University, Philadelphia, PA 19122, United States;3. Department of Mathematics, Texas A&M University, College Station, TX 77843, United States
Abstract:Over a field of prime characteristic p>2, we prove that the cohomology rings of some pointed Hopf algebras of dimension p3 are finitely generated. These are Hopf algebras arising in the ongoing classification of finite dimensional pointed Hopf algebras in positive characteristic. They include bosonizations of Nichols algebras of Jordan type in a general setting. When p=3, we also consider their Hopf algebra liftings, that is Hopf algebras whose associated graded algebra with respect to the coradical filtration is given by such a bosonization. Our proofs are based on an algebra filtration and a lemma of Friedlander and Suslin, drawing on both twisted tensor product resolutions and Anick resolutions to locate the needed permanent cocycles in May spectral sequences.
Keywords:16E05  16E40  16T05
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