Twisted unipotent groups
Ken A. Brown, Shlomo Gelaki

TL;DR
This paper investigates the structure and representation theory of twisted Hopf algebras associated with unipotent algebraic groups, revealing their layered algebraic composition and classifying their simple modules.
Contribution
It introduces a detailed structural description of twisted Hopf algebras for unipotent groups and classifies their simple modules, highlighting new algebraic and representation-theoretic insights.
Findings
Twisted Hopf algebras are involutive n-step iterated Hopf Ore extensions.
Simple modules are parametrized by double cosets and are all 1-dimensional.
The group of simple modules is explicitly identified as a closed subgroup of G.
Abstract
We study the algebraic structure and representation theory of the Hopf algebras when is an affine algebraic unipotent group over with and is a Hopf -cocycle for . The cotriangular Hopf algebras have the same coalgebra structure as but a deformed multiplication. We show that they are involutive -step iterated Hopf Ore extensions of derivation type. The 2-cocycle has as support a closed subgroup of , and is a crossed product , where is the Lie algebra of and is a deformed coideal subalgebra. The simple -modules are stratified by a family of factor algebras , parametrised by the double cosets of in . The finite dimensional simple…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research
