A Connected Complex Simple Centerfree Lie Group whose Exponential Function is not Surjective

Key Points

• The aim is to provide an example of a complex simple Lie group where the exponential function fails to be surjective.
• Analysis of properties of complex simple Lie groups
• Examination of the exponential map characteristics
• Identification of groups with trivial centers
• Identified a complex simple Lie group G with dimension 10
• Demonstrated that the exponential map of G is not surjective
• Highlighted the implications of non-surjectivity in group characteristics