Poguntke, Detlev
Detlev
Poguntke
Symmetry and nonsymmetry for a class of exponential Lie groups
1980
2018-07-24T12:58:03Z
2018-07-24T12:58:03Z
journal_article
https://pub.uni-bielefeld.de/record/1775493
https://pub.uni-bielefeld.de/record/1775493.json
urn:nbn:de:0070-bipr-9108
bytes
application/pdf
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.