Abstract
We study the relations of Hartmann and unitary uniform distribution in solvable groups, in particular in semidirect products of Abelian groups. In every nilpotent group these notions of uniform distribution coincide, but, in general, they are different in solvable groups, as is demonstrated by the motion group of the plane. However, we show that Hartmann and unitary uniform distribution coincide in every solvable analytic group whose Lie algebra has no purely imaginary roots. Finally, we give two six-dimensional solvable analytic groups with the same set of roots, such that the concepts of uniform distribution coincide in one group and differ in the other.
Keywords
- Semidirect Product
- Solvable Group
- Compact Abelian Group
- Imaginary Root
- Strong Operator Topology
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Dedicated to Professor Elmar Thoma on the occasion of his 60th birthday
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© 1986 Springer-Verlag
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Gröchenig, K., Losert, V., Rindler, H. (1986). Uniform distribution in solvable groups. In: Heyer, H. (eds) Probability Measures on Groups VIII. Lecture Notes in Mathematics, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077176
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DOI: https://doi.org/10.1007/BFb0077176
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16806-5
Online ISBN: 978-3-540-44852-5
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