Finite generation of some cohomology rings via twisted tensor product and Anick resolutions Academic Article

abstract

• 2018 Elsevier B.V. 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.

authors

• Witherspoon, Sarah

published proceedings

• Journal of Pure and Applied Algebra

author list (cited authors)

• Van C. Nguyen, .., Wang, X., & Witherspoon, S.

citation count

• 3

complete list of authors

• Wang, Xingting||Witherspoon, Sarah

publication date

• January 2019

publisher

• Elsevier  Publisher

published in

• Journal of Pure and Applied Algebra  Journal

Digital Object Identifier (DOI)

• 10.1016/j.jpaa.2018.03.012

start page

• 316

end page

• 339

volume

• 223

issue

• 1

URL

• http://dx.doi.org/10.1016/j.jpaa.2018.03.012