@article{1775493,
abstract = {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.},
author = {Poguntke, Detlev},
issn = {0075-4102},
journal = {Journal für die reine und angewandte Mathematik},
pages = {127--138},
title = {{Symmetry and nonsymmetry for a class of exponential Lie groups}},
volume = {315},
year = {1980},
}