Coordinate rings of prounipotent groups (Q1078328)

In the setting of algebraic groups, unipotent groups are the analogues of nilpotent groups. For such groups U over an algebraically closed field k of characteristic 0, the coordinate ring k[U] is both a polynomial algebra and a rational U-module (actually a bi-U-module). The main point of the present work is to related these structures by selecting suitable algebra generators adapated to the ascending socle series. The explanation is carried out in the more general context of prounipotent groups H. The assumption of characteristic 0 and the assumption of algebraic closure permits the use of a mixture of techniques from algebraic groups as well as Lie theory. The detailed results are too complicated to summarize since a number of concepts and notations would have to be explained along the way.