Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.05267

On the finite generation of the cohomology of bosonizations

Nicolás Andruskiewitsch·David Jaklitsch·Van C. Nguyen·Amrei Oswald·Julia Plavnik·Anne V. Shepler·Xingting Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable finite-dimensional Hopf algebras have finitely generated cohomology. In fact, our results are shown in more generality for smash products. As applications, we prove the bosonizations of some Nichols algebras (such as Nichols algebras of diagonal type, the restricted Jordan plane, Nichols algebras of direct sums of Jordan blocks plus points labeled with 1), by some suitable finite-dimensional Hopf algebras, have finitely generated cohomology, recovering some known results as well as providing new examples.

Explore related subjects

math.QAmath.KTmath.RA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nicolás Andruskiewitsch, David Jaklitsch, Van C. Nguyen, Amrei Oswald, Julia Plavnik, Anne V. Shepler, Xingting Wang. 2025-06-05. On the finite generation of the cohomology of bosonizations. https://doi.org/10.1016/j.jalgebra.2025.10.057

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Categorification of quasi-split iquantum groups

We introduce a new family of graded 2-categories generalizing the 2-quantum groups introduced by Khovanov, Lauda and Rouquier. We use them to categorify quasi-split iquantum groups in all symmetric types.

math.QA↗
arXiv2026

The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid

In a previous article, we showed that local projectivity is a sufficient condition for the existence of a bialgebroid structure on the ring of differential operators on an affine variety. In this note, we show using elementary methods that the ring of differential operators on a nodal curve is neither locally projective nor does it admit a bialgebroid structure.

math.QA↗
arXiv2026

Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction

We give complete conjugacy classes of modular group SL(2,Z). Particularly, the conjugacy classes of hyperbolic elements are decided by the proper equivalence classes of indefinite forms, and we give an example. Finally, we describe the coset representatives of centralizer of S, ST, T and hyperbolic elements of SL(2,Z) by regular continued fraction. In conclusion, most Nichols algebras over modular group are infinite-dimensional except Proposition 4.10.

math.QA↗