On the surjectivity of the exponential function of complex algebraic, complex semisimple, and complex splittable Lie groups
type: Item
instance of: scholarly article
title: On the surjectivity of the exponential function of complex algebraic, complex semisimple, and complex splittable Lie groups
zbMATH Open document ID: 0870.22004
author: Michael Wüstner
published in: Journal of Algebra
publication date: 1997-08-25T00:00:00Z
review text: The author studies the surjectivity of the exponential function for complex algebraic (in particular, complex semisimple) Lie groups. The main result is that for complex algebraic, or more generally, complex splittable Lie groups the surjectivity of the exponential function is equivalent to the connectedness in the Lie group of the centralizers of the nilpotent elements in the Lie algebra. This implies that the only complex semisimple Lie groups with surjective exponential function are isomorphic to finite products of the adjoint groups of SL\((n,{\mathbb C})\).
Mathematics Subject Classification ID: 22E10
Mathematics Subject Classification ID: 20G20
zbMATH DE Number: 941281
zbMATH Keywords: complex algebraic Lie group
zbMATH Keywords: exponential function
zbMATH Keywords: splittable Lie group
reviewed by: Jimmie D. Lawson
MaRDI profile type: Publication
full work available at URL: jabr.1996.0300
OpenAlex ID: W2116827939
Wikidata QID: Q115396081
DOI: 10.1006/JABR.1996.0300
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description: scientific article; zbMATH DE number 941281