Examples of groups which are not weakly amenable
نویسندگان
چکیده
منابع مشابه
Weakly Amenable Groups
In the present paper we construct the first examples of finitely generated non–amenable groups whose left regular representations are not uniformly isolated from the trivial representation.
متن کاملAre Unitarizable Groups Amenable?
We give a new formulation of some of our recent results on the following problem: if all uniformly bounded representations on a discrete group G are similar to unitary ones, is the group amenable? In §5, we give a new proof of Haagerup's theorem that, on non-commutative free groups, there are Herz-Schur multipliers that are not coefficients of uniformly bounded representations. We actually prov...
متن کاملWhich groups are amenable to proving exponent two for matrix multiplication?
The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\omega$ and is conjectured to be powerful enough to prove $\omega = 2$, although finding a suitable g...
متن کاملAmenable Groups
Throughout we let Γ be a discrete group. For f : Γ → C and each s ∈ Γ we define the left translation action by (s.f)(t) = f(s−1t). Definition 1.1. A group Γ is amenable is there exists a state μ on l∞(Γ) which is invariant under the left translation action: for all s ∈ Γ and f ∈ l∞(Γ), μ(s.f) = μ(f). Example 1.2. Finite groups are amenable: take the state which sends χ{s} to 1 |Γ| for each s ∈ ...
متن کاملDoubly Transitive Permutation Groups Which Are Not Doubly Primitive
Hypothesis (A): G is a doubly transitive permutation group on a set Q. For 01 E Q, G, has a set Z = {B, , B, ,..., B,}, t > 2, which is a complete set of imprimitivity blocks on Q {a}. Let j Bi / = b > 1 for all i. Denote by H the kernel of G, on .Z and by Ki and K< the subgroups of G, fixing Bi setwise and pointwise respectively, 1 .< i < t. Let /3 E Bl . Here j Q j = 1 + ht. M. D. Atkinson ha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 2012
ISSN: 2156-2261
DOI: 10.1215/21562261-1550985