35 research outputs found
Return words of linear involutions and fundamental groups
We investigate the natural codings of linear involutions. We deduce from the
geometric representation of linear involutions as Poincar\'e maps of measured
foliations a suitable definition of return words which yields that the set of
first return words to a given word is a symmetric basis of the free group on
the underlying alphabet . The set of first return words with respect to a
subgroup of finite index of the free group on is also proved to be a
symmetric basis of
Partial projective representations and the partial Schur multiplier: a survey
We present a short survey on partial projective representations, the partial Schur multiplier and related notions
Examples of weakly amenable discrete quantum groups
We prove that Wang's free orthogonal and free unitary quantum groups are
weakly amenable and that their Cowling-Haagerup constant is equal to 1. This is
achieved by estimating the completely bounded norm of the projections on the
coefficients of irreducible representations of their compact duals. An argument
of monoidal equivalence then allows us to extend this result to quantum
automorphism groups of finite spaces and even yields some examples of weakly
amenable non-unimodular discrete quantum groups with the Haagerup property.Comment: 25 page