2024/07/09 by Ken A. Brown, Shlomo Gelaki, Brown, Ken A. +1
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2407.07005
openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the algebraic structure and representation theory of the Hopf algebras JO(G)J when G is an affine algebraic unipotent group over ℂ with dim(G) = n and J is a Hopf 2-cocycle for G. The cotriangular Hopf algebras JO(G)J have the same coalgebra structure as O(G) but a deformed multiplication. We show that they are involutive n-step iterated Hopf Ore extensions of derivation type. The 2-cocycle J has as support a closed subgroup T of G, and JO(G)J is a crossed product S #σU(\mathfrakt), where \mathfrakt is the Lie algebra of T and S is a deformed coideal subalgebra. The simple JO(G)J-modules are stratified by a family of factor algebras JO(Zg)J, parametrised by the double cosets TgT of T in G. The finite dimensional simple JO(G)J-modules are all 1-dimensional, so form a group Γ, which we prove to be an explicitly determined closed subgroup of G. A selection of examples illustrate our results.