18,919 research outputs found
Haagerup property for C*-algebras and rigidity of C*-algebras with property (T)
We study the Haagerup property for C*-algebras. We first give new examples of
C*-algebras with the Haagerup property. A nuclear C*-algebra with a faithful
tracial state always has the Haagerup property, and the permanence of the
Haagerup property for C*-algebras is established. As a consequence, the class
of all C*-algebras with the Haagerup property turns out to be quite large. We
then apply Popa's results and show the C*-algebras with property (T) have a
certain rigidity property. Unlike the case of von Neumann algebras, for the
reduced group C*-algebras of groups with relative property (T), the rigidity
property strongly fails in general. Nevertheless, for some groups without
nontrivial property (T) subgroups, we show a rigidity property in some cases.
As examples, we prove the reduced group C*-algebras of the (non-amenable)
affine groups of the affine planes have a rigidity property.Comment: This is the final version. 22pages, no figure
Suzuki-invariant codes from the Suzuki curve
In this paper we consider the Suzuki curve over
the field with elements. The automorphism group of this curve is
known to be the Suzuki group with elements. We
construct AG codes over from a -invariant divisor
, giving an explicit basis for the Riemann-Roch space for . These codes then have the full Suzuki group as their
automorphism group. These families of codes have very good parameters and are
explicitly constructed with information rate close to one. The dual codes of
these families are of the same kind if
From Thompson to Baer-Suzuki: a sharp characterization of the solvable radical
We prove that an element of prime order belongs to the solvable
radical of a finite (or, more generally, a linear) group if and only if
for every the subgroup generated by is solvable. This
theorem implies that a finite (or a linear) group is solvable if and only
if in each conjugacy class of every two elements generate a solvable
subgroup.Comment: 28 page
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