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arXiv · 1710.07141

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

Van C. Nguyen·Xingting Wang·Sarah Witherspoon
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Abstract

Over a field of prime characteristic $p>2$, we prove that the cohomology rings of some pointed Hopf algebras of dimension $p^3$ are finitely generated. These are Hopf algebras arising in the ongoing classification of finite dimensional Hopf algebras in positive characteristic, and include bosonizations of Nichols algebras of Jordan type in a general setting as well as their liftings when $p=3$. Our techniques are applications of twisted tensor product resolutions and Anick resolutions in combination with May spectral sequences.

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Van C. Nguyen, Xingting Wang, Sarah Witherspoon. 2017-10-19. Finite generation of some cohomology rings via twisted tensor product and Anick resolutions. https://arxiv.org/abs/1710.07141

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