The structure of complex Lie groups (Q2756691)

These lecture notes provide an introduction to general properties of complex Lie groups, without using the theory of real Lie groups. NEWLINENEWLINENEWLINEThe main tool is the theory of (analytic) representative functions, i.e. functions on the group whose left (or right) translates span a finite-dimensional vector space of functions. NEWLINENEWLINENEWLINEThe topics presented are the Hopf algebra of representative functions, extension of representations from a complex Lie subgroup to the entire group, structure of complex Lie groups, algebraic subgroups of complex Lie groups and observability in complex Lie groups (extendability of rational representations from a subgroup to the entire group). NEWLINENEWLINENEWLINETwo appendices are devoted, without proofs, to the elementary theory of Lie algebras (including a heuristic presentation of the Campbell-Hausdorff formula) and to basic properties of pro-affine algebraic groups.