Variants of a-T-menability for actions on non-commutative Lp spaces

Baptiste Olivier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on non-commutative Lp spaces. We introduce a variant (H_Lp) for orthogonal representations with vanishing coefficients on Lp, and study its relationships with property (H). We also give a characterization of (H) by the means of strongly mixing actions on a non-commutative Lp space. We construct proper actions of groups with (H) by affine isometries on some non-commutative Lp space, such as the Lp space associated to the hyperfinite II infinite factor.

Mots clés: a-T-menabilty; non-commutative Lp spaces; orthogonal group representations; property (H); proper actions by affine isometries

Domaines: Théorie des groupes [math.GR]

Baptiste Olivier. Variants of a-T-menability for actions on non-commutative Lp spaces. 2013. ⟨hal-00815699⟩