TY - JOUR
AB - This paper is a contribution to the question for which simply connected Lie groups G the group algebra L to the power of 1(G) is symmetric (=hermitean). For groups G in a certain subclass of the class of exponential Lie groups a necessary and sufficient condition for the symmetry of L to the power of 1(G) is given in terms of the Lie algebra of G. This subclass contains all groups with Lie algebra g such that the (additive) Jordan decomposition is possible in ad(g). The condition was introduced by Boidol in exploring the *-primitve ideal space, and so the main result of the paper implies that for some exponential Lie groups G the symmetry of L to the power of 1(G) is equivalent to a certain property of the *-primitive ideal space. Moreover, an example of a seven-dimensional exponential Lie group G with symmetric group algebra is given where the existing general methods are not applicable to get the symmetry.
AU - Poguntke, Detlev
ID - 1775493
JF - Journal für die reine und angewandte Mathematik
SN - 0075-4102
TI - Symmetry and nonsymmetry for a class of exponential Lie groups
VL - 315
ER -