The Weak Haagerup Property II: Examples
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The Weak Haagerup Property II : Examples. / Haagerup, Uffe; Knudby, Søren.
In: International Mathematics Research Notices, Vol. 2015, No. 16, 2015, p. 6941-6967.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The Weak Haagerup Property II
T2 - Examples
AU - Haagerup, Uffe
AU - Knudby, Søren
PY - 2015
Y1 - 2015
N2 - The weak Haagerup property for locally compact groups and the weak Haagerup constant were recently introduced by the second author [27]. The weak Haagerup property is weaker than both weak amenability introduced by Cowling and the first author [9] and the Haagerup property introduced by Connes [6] and Choda [5]. In this paper, it is shown that a connected simple Lie group G has the weak Haagerup property if and only if the real rank of G is zero or one. Hence for connected simple Lie groups the weak Haagerup property coincides with weak amenability. Moreover, it turns out that for connected simple Lie groups the weak Haagerup constant coincides with the weak amenability constant, although this is not true for locally compact groups in general. It is also shown that the semidirect product R2 × SL(2,R) does not have the weak Haagerup property.
AB - The weak Haagerup property for locally compact groups and the weak Haagerup constant were recently introduced by the second author [27]. The weak Haagerup property is weaker than both weak amenability introduced by Cowling and the first author [9] and the Haagerup property introduced by Connes [6] and Choda [5]. In this paper, it is shown that a connected simple Lie group G has the weak Haagerup property if and only if the real rank of G is zero or one. Hence for connected simple Lie groups the weak Haagerup property coincides with weak amenability. Moreover, it turns out that for connected simple Lie groups the weak Haagerup constant coincides with the weak amenability constant, although this is not true for locally compact groups in general. It is also shown that the semidirect product R2 × SL(2,R) does not have the weak Haagerup property.
U2 - 10.1093/imrn/rnu132
DO - 10.1093/imrn/rnu132
M3 - Journal article
AN - SCOPUS:84954223470
VL - 2015
SP - 6941
EP - 6967
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 16
ER -
ID: 161589476