Hun Hee Lee

Projectivity of modules over Fourier algebras

In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective in the category of operator spaces. We will show that pro- jectivity often implies that the underlying group is discrete and give evidence to show that amenability also plays an important role. Over the past thirty years there has been a rich body of work dedicated to understanding the cohomological properties of the various Banach algebras arising in the study of locally compact groups. The seminal paper in this respect is certainly Barry Johnsons memoir (22) in which he introduces the concept of amenability for a Banach algebra, and shows that for a locally compact group G the group algebra L 1 (G) is amenable if and only if G is amenable in the classical sense. While applications of cohomology to harmonic anlysis may be more celebrated, there have also been a number of significant studies related to the homological properties of the algebras arising from groups. Recently, H. G. Dales and M. E. Polyakov (12) gave a detailed study of the homological properties of modules over the group algebra of a locally compact group. In their work they focused primarily on the question of whether or not certain natural left L 1 (G)-modules are respectively projective, injective, or flat. They were able to show, for example, that when viewed as the dual left-module of L 1 (G), L ∞ (G) is projective precisely when the group G is finite. In stark contrast, they prove that L ∞ (G) is always injective. They also showed that the measure algebra M(G) is projective precisely when G is discrete, while in this case injectivity is equivalent to the group G being amenable. When G is abelian the classical Fourier transform identifies L 1 (G) with a com-

Some Weighted Group Algebras are Operator Algebras

Let

Integration over the quantum diagonal subgroup and associated Fourier-like algebras

G

Dimensions of components of tensor products of representations of linear groups with applications to Beurling–Fourier algebras

be a finitely generated group with polynomial growth, and let

New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups

\om

DISTANCE-k GRAPHS OF HYPERCUBE AND q-HERMITE POLYNOMIALS

be a weight, i.e. a sub-multiplicative function on

HYPERCONTRACTIVITY ON THE q-ARAKI-WOODS ALGEBRAS

G

Beurling–Fourier algebras, operator amenability and Arens regularity

with positive values. We study when the weighted group algebra

Type and cotype of operator spaces

\ell^1(G,\om)

Duality of Fourier type with respect to locally compact abelian groups

is isomorphic to an operator algebra. We show that