共查询到20条相似文献,搜索用时 31 毫秒
1.
Takeshi Katsura 《Journal of Functional Analysis》2009,257(5):1589-127
We give various necessary and sufficient conditions for an AF-algebra to be isomorphic to a graph C∗-algebra, an Exel-Laca algebra, and an ultragraph C∗-algebra. We also explore consequences of these results. In particular, we show that all stable AF-algebras are both graph C∗-algebras and Exel-Laca algebras, and that all simple AF-algebras are either graph C∗-algebras or Exel-Laca algebras. In addition, we obtain a characterization of AF-algebras that are isomorphic to the C∗-algebra of a row-finite graph with no sinks. 相似文献
2.
We show that the graph construction used to prove that a gauge-invariant ideal of a graph C ???-algebra is isomorphic to a graph C ???-algebra, and also used to prove that a graded ideal of a Leavitt path algebra is isomorphic to a Leavitt path algebra, is incorrect as stated in the literature. We give a new graph construction to remedy this problem, and prove that it can be used to realize a gauge-invariant ideal (respectively, a graded ideal) as a graph C ???-algebra (respectively, a Leavitt path algebra). 相似文献
3.
We show that a number of naturally occurring comparison relations on positive elements in a C?-algebra are equivalent to natural comparison properties of their corresponding open projections in the bidual of the C?-algebra. In particular we show that Cuntz comparison of positive elements corresponds to a comparison relation on open projections, that we call Cuntz comparison, and which is defined in terms of—and is weaker than—a comparison notion defined by Peligrad and Zsidó. The latter corresponds to a well-known comparison relation on positive elements defined by Blackadar. We show that Murray-von Neumann comparison of open projections corresponds to tracial comparison of the corresponding positive elements of the C?-algebra. We use these findings to give a new picture of the Cuntz semigroup. 相似文献
4.
Richard H Herman 《Journal of Functional Analysis》1975,20(3):234-239
In this note we discuss various extensions of a normal 1 derivation of a uniformly hyperfinite C1-algebra. Various approximation theorems are employed to show when said extensions generate automorphism groups of the C1-algebra. We characterize the “maximal” extension of Sakai and Powers as a graph limit and show when this extension is the closure of the given derivation. We also discuss an identity obeyed by the resolvent of a derivation. 相似文献
5.
We prove that a graph C
*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact
sequence in K-theory. We prove that a similar classification also holds for a graph C
*-algebra with a largest proper ideal that is an AF-algebra. Our results are based on a general method developed by the first
named author with Restorff and Ruiz. As a key step in the argument, we show how to produce stability for certain full hereditary
subalgebras associated to such graph C
*-algebras. We further prove that, except under trivial circumstances, a unique proper nontrivial ideal in a graph C
*-algebra is stable. 相似文献
6.
Hiroshi Takai 《Journal of Functional Analysis》1975,19(1):25-39
Let be a C1-algebra, and G be a locally compact abelian group. Suppose α is a continuous action of G on . Then there exists a continuous action ga of the dual group of G on the C1-crossed product by α such that the C1-crossed product is isomorphic to the tensor product and the C1-algebra of all compact operators on L2(G). 相似文献
7.
Alexander Alldridge 《Journal of Functional Analysis》2007,249(2):425-453
We study multivariate generalisations of the classical Wiener-Hopf algebra, which is the C∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C∗-algebra is known to be isomorphic to the reduced C∗-algebra of a certain restricted action groupoid, given by the action of Euclidean space on a certain compactification. Using groupoid methods, we construct composition series for the Wiener-Hopf C∗-algebra by a detailed study of this compactification. We compute the spectrum, and express homomorphisms in K-theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms. Namely, these symbols maps turn out to be given by an analytical family index of a continuous family of Fredholm operators. In a subsequent paper, we also obtain a topological expression of these indices. 相似文献
8.
We consider the Deaconu–Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of the associated groupoid C ?-algebra. For a special class of actions we describe the Jacobson topology. 相似文献
9.
10.
BIPUL SAURABH 《Proceedings Mathematical Sciences》2017,127(1):133-164
For the quantum symplectic group SP q (2n), we describe the C ?-algebra of continuous functions on the quotient space S P q (2n)/S P q (2n?2) as an universal C ?-algebra given by a finite set of generators and relations. The proof involves a careful analysis of the relations, and use of the branching rules for representations of the symplectic group due to Zhelobenko. We then exhibit a set of generators of the K-groups of this C ?-algebra in terms of generators of the C ?-algebra. 相似文献
11.
We prove that the full C ?-algebra of a second-countable, Hausdorff, étale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G has totally disconnected unit space, then the complex ?-algebra of its inverse semigroup of compact open bisections, as introduced by Steinberg, is simple if and only if G is both effective and minimal. 相似文献
12.
13.
Alan L.T. Paterson 《Journal of Functional Analysis》2008,255(6):1458-1479
The paper establishes, for a wide class of locally compact groupoids Γ, the E-theoretic descent functor at the C∗-algebra level, in a way parallel to that established for locally compact groups by Guentner, Higson and Trout. Section 2 shows that Γ-actions on a C0(X)-algebra B, where X is the unit space of Γ, can be usefully formulated in terms of an action on the associated bundle B?. Section 3 shows that the functor B→C∗(Γ,B) is continuous and exact, and uses the disintegration theory of J. Renault. Section 4 establishes the existence of the descent functor under a very mild condition on Γ, the main technical difficulty involved being that of finding a Γ-algebra that plays the role of Cbcont(T,B) in the group case. 相似文献
14.
We discuss a synchronization property for subshifts, that we call λ-synchronization. Under an irreducibility assumption we associate to a λ-synchronizing subshift a simple C ?-algebra. 相似文献
15.
Alexander Alldridge 《Advances in Mathematics》2008,218(1):163-201
We study the multivariate generalisation of the classical Wiener-Hopf algebra, which is the C∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C∗-algebra is known to be isomorphic to the reduced C∗-algebra of a certain restricted action groupoid. It admits a composition series, and therefore, a ‘symbol’ calculus. Using groupoid methods, we obtain, in the framework of Kasparov's bivariant KK-theory, a topological expression of the index maps associated to these symbol maps in terms of geometric-topological data of the underlying convex cone. This generalises an index theorem by Upmeier concerning Wiener-Hopf operators on symmetric cones. Our result covers a wide class of cones containing polyhedral and homogeneous cones. 相似文献
16.
A. Chigogidze 《Topology and its Applications》2010,157(4):774-863
We give a short answer to the question in the title: dendrits. Precisely we show that the C*-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category C1 of all (not necessarily commutative) unital C*-algebras if and only if X is an absolute retract of dimension dimX?1 or, equivalently, that X is a dendrit. 相似文献
17.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(3):293-295
We show that the C* -algebra of the regular representation of a discrete group G onto a subset Σ of G is the reduced C* -algebra of an r-discrete groupoid whose space of units is totally disconnected and contains Σ as a dense subset. The C*-algebra of quasicrystals, some Cuntz-Krieger and crossed product algebras, and Wiener-Hopf algebras are particular cases of this construction 相似文献
18.
Marcelo Laca 《Journal of Functional Analysis》2011,261(1):169-187
We complete the analysis of KMS-states of the Toeplitz algebra T(N?N×) of the affine semigroup over the natural numbers, recently studied by Raeburn and the first author, by showing that for every inverse temperature β in the critical interval 1?β?2, the unique KMSβ-state is of type III1. We prove this by reducing the type classification from T(N?N×) to that of the symmetric part of the Bost-Connes system, with a shift in inverse temperature. To carry out this reduction we first obtain a parametrization of the Nica spectrum of N?N× in terms of an adelic space. Combining a characterization of traces on crossed products due to the second author with an analysis of the action of N?N× on the Nica spectrum, we can also recover all the KMS-states of T(N?N×) originally computed by Raeburn and the first author. Our computation sheds light on why there is a free transitive circle action on the extremal KMSβ-states for β>2 that does not ostensibly come from an action of T on the C?-algebra. 相似文献
19.
20.
《Journal of Functional Analysis》1987,72(1):151-181
A definition of a completely bounded multilinear operator from one C1-algebra into another is introduced. Each completely bounded multilinear operator from a C1-algebra into the algebra of bounded linear operators on a Hilbert space is shown to be representable in terms of 1-representations of the C1-algebra and interlacing operators. This result extends Wittstock's Theorem that decomposes a completely bounded linear operator from a C1-algebra into an injective C1-algebra into completely positive linear operators. 相似文献