Dense images of the power maps for a disconnected real algebraic group

Article Type

Research Article

Publication Title

Journal of Group Theory

Abstract

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.

First Page

973

Last Page

985

DOI

10.1515/jgth-2020-0152

Publication Date

9-1-2021

Comments

Open Access, Green

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