Symmetry and nonsymmetry for a class of exponential Lie groups

Poguntke D (1980)
Journal für die reine und angewandte Mathematik 315: 127-138.

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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.
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Poguntke D. Symmetry and nonsymmetry for a class of exponential Lie groups. Journal für die reine und angewandte Mathematik. 1980;315:127-138.
Poguntke, D. (1980). Symmetry and nonsymmetry for a class of exponential Lie groups. Journal für die reine und angewandte Mathematik, 315, 127-138.
Poguntke, D. (1980). Symmetry and nonsymmetry for a class of exponential Lie groups. Journal für die reine und angewandte Mathematik 315, 127-138.
Poguntke, D., 1980. Symmetry and nonsymmetry for a class of exponential Lie groups. Journal für die reine und angewandte Mathematik, 315, p 127-138.
D. Poguntke, “Symmetry and nonsymmetry for a class of exponential Lie groups”, Journal für die reine und angewandte Mathematik, vol. 315, 1980, pp. 127-138.
Poguntke, D.: Symmetry and nonsymmetry for a class of exponential Lie groups. Journal für die reine und angewandte Mathematik. 315, 127-138 (1980).
Poguntke, Detlev. “Symmetry and nonsymmetry for a class of exponential Lie groups”. Journal für die reine und angewandte Mathematik 315 (1980): 127-138.
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