450 research outputs found
Primeness, semiprimeness and localisation in Iwasawa algebras
Necessary and sufficient conditions are given for the completed group
algebras of a compact p-adic analytic group with coefficient ring the p-adic
integers or the field of p elements to be prime, semiprime and a domain.
Necessary and sufficient conditions for the localisation at semiprime ideals
related to the augmentation ideals of closed normal subgroups are found. Some
information is obtained about the Krull and global dimensions of the
localisations. The results extend and complete work of A. Neumann and J. Coates
et al
Examples of groups which are not weakly amenable
We prove that weak amenability of a locally compact group imposes a strong
condition on its amenable closed normal subgroups. This extends non weak
amenability results of Haagerup (1988) and Ozawa--Popa (2010). A von Neumann
algebra analogue is also obtained.Comment: 10 pages; some remarks are clarified (v2
Induction in stages for crossed products of C*-algebras by maximal coactions
Let B be a C*-algebra with a maximal coaction of a locally compact group G,
and let N and H be closed normal subgroups of G with N contained in H. We show
that the process Ind_(G/H)^G which uses Mansfield's bimodule to induce
representations of the crossed product of B by G from those of the restricted
crossed product of B by (G/H) is equivalent to the two-stage induction process:
Ind_(G/N)^G composed with Ind_(G/H)^(G/N). The proof involves a calculus of
symmetric imprimitivity bimodules which relates the bimodule tensor product to
the fibred product of the underlying spaces.Comment: 38 pages, LaTeX, uses Xy-pic; significant reorganization of previous
version; short section on regularity of induced representations adde
A Galois correspondence for compact group actions on C*-algebras
In this paper, we prove a Galois correspondence for compact group actions on
C*-algebras in the presence of a commuting minimal action. Namely, we show that
there is a one to one correspondence between the C*-subalgebras that are
globally invariant under the compact action and the commuting minimal action,
that in addition contain the fixed point algebra of the compact action and the
closed, normal subgroups of the compact group
Decomposing locally compact groups into simple pieces
We present a contribution to the structure theory of locally compact groups.
The emphasis is on compactly generated locally compact groups which admit no
infinite discrete quotient. It is shown that such a group possesses a
characteristic cocompact subgroup which is either connected or admits a
non-compact non-discrete topologically simple quotient. We also provide a
description of characteristically simple groups and of groups all of whose
proper quotients are compact. We show that Noetherian locally compact groups
without infinite discrete quotient admit a subnormal series with all
subquotients compact, compactly generated Abelian, or compactly generated
topologically simple. Two appendices introduce results and examples around the
concept of quasi-product.Comment: Index added; minor change
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