Dense images of the power maps for a disconnected real algebraic group
Journal of Group Theory
Let G be a complex algebraic group defined over R, which is not necessarily Zariski-connected. In this article, we study the density of the images of the power maps g → gk, k ∈ N, on real points of G, i.e., GR equipped with the real topology. As a result, we extend a theorem of P. Chatterjee on surjectivity of the power map for the set of semisimple elements of GR. We also characterize surjectivity of the power map for a disconnected group GR. The results are applied in particular to describe the image of the exponential map of GR.
Mandal, Arunava, "Dense images of the power maps for a disconnected real algebraic group" (2021). Journal Articles. 1821.
Open Access, Green