On the representation radical of complex Lie groups (Q1911649)

For a complex Lie group \(G\), the representation radical \(N(G)\) is defined as the intersection of the kernels of all finite dimensional semisimple analytic representations of \(G\). The authors study the connectedness of \(N(G)\) for a class of nonconnected complex Lie groups. They also prove, for the same class, that the algebraic kernel of \(G\) introduced in their previous work [ibid. 173, 166-179 (1995; Zbl 0833.22022)] is equal to \(N(G)H\), where \(H\) is any maximal reductive analytic subgroup of the identity component \(G_0\).