Relative Property (T) for Nilpotent Subgroups
| Autor: | Indira Chatterji, Dave Witte Morris, Riddhi Shah |
|---|---|
| Přispěvatelé: | Université Côte d'Azur (UCA) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
010102 general mathematics Group Theory (math.GR) almost-invariant vector 16. Peace & justice 01 natural sciences Mathematics::Group Theory 2000 Mathematics Subject Classification: 22D10. Keywords and Phrases: relative Property (T) nilpotent subgroup 0103 physical sciences FOS: Mathematics fibered tensor product 010307 mathematical physics 0101 mathematics Representation Theory (math.RT) [MATH]Mathematics [math] 22D10 Mathematics - Group Theory Mathematics - Representation Theory |
| Zdroj: | Documenta Mathematica Documenta Mathematica, Universität Bielefeld, 2018 |
| ISSN: | 1431-0643 1431-0635 |
| Popis: | We show that relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself. This and other results are a consequence of a theorem of independent interest, which states that if $H$ is a closed subgroup of a locally compact group~$G$, and $A$ is a closed subgroup of the center of~$H$, such that $A$ is normal in~$G$, and $(G/A, H/A)$ has relative Property (T), then $(G, H^{(1)})$ has relative Property (T), where $H^{(1)}$ is the closure of the commutator subgroup of~$H$. In fact, the assumption that $A$ is in the center of~$H$ can be replaced with the weaker assumption that $A$~is abelian and every $H$-invariant finite measure on the unitary dual of~$A$ is supported on the set of fixed points. Documenta Mathematica, 2018, vol. 23, p. 353-382, 1431-0643 |
| Databáze: | OpenAIRE |
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