Twisting of affine algebraic groups, II

Abstract We use [11] to study the algebra structure of twisted cotriangular Hopf algebras ${}_J\mathcal{O}(G)_{J}$, where $J$ is a $2$-cocycle for connected nilpotent algebraic group $G$ over $\mathbb{C}$. In particular, we show that ${}_J\mathcal{O}(G)_{J}$ an affine Noetherian domain with Gelfand–Kirillov dimension $\dim (G)$, and if unipotent supported on $G$, then ${}_J\mathcal{O}(G)_{J}\cong U({\mathfrak{g}})$ as algebras, ${\mathfrak{g}}={\textrm{Lie}}(G)$. also determine finite dimensional irreducible representations by analyzing function $(H,H)$-double cosets support $H\subset G$ $J$. Finally, work out several examples illustrate our results.