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.
DA  - 1980
DO  - 10.1515/crll.1980.315.127
LA  - eng
M2  - 127
PY  - 1980
SN  - 0075-4102
SP  - 127-138
T2  - Journal für die reine und angewandte Mathematik
TI  - Symmetry and nonsymmetry for a class of exponential Lie groups
UR  - https://nbn-resolving.org/urn:nbn:de:0070-bipr-9108
Y2  - 2024-11-22T07:08:06
ER  -