共查询到20条相似文献,搜索用时 15 毫秒
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《Journal of Pure and Applied Algebra》2023,227(3):107207
We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain a complete characterization of congruence-simpleness for Steinberg algebras of second-countable ample groupoids, extending the well-known characterizations when S is a field. We apply our congruence-simplicity results to tight groupoids of inverse semigroup representations associated to self-similar graphs. 相似文献
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For a certain class of extensions of C*-algebras in which B and A belong to classifiable classes of C*-algebras, we show that the functor which sends to its associated six term exact sequence in K-theory and the positive cones of K0(B) and K0(A) is a classification functor. We give two independent applications addressing the classification of a class of C*-algebras arising from substitutional shift spaces on one hand and of graph algebras on the other. The former application leads to the answer of a question of Carlsen and the first named author concerning the completeness of stabilized Matsumoto algebras as an invariant of flow equivalence. The latter leads to the first classification result for nonsimple graph C*-algebras. 相似文献
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Marius Dadarlat 《Advances in Mathematics》2009,222(5):1850-2880
Let X be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of C(X)-algebras by C(X)-subalgebras with controlled complexity. The following applications are given. All unital separable continuous fields of C*-algebras over X with fibers isomorphic to a fixed Cuntz algebra On, n∈{2,3,…,∞}, are locally trivial. They are trivial if n=2 or n=∞. For n?3 finite, such a field is trivial if and only if (n−1)[A1]=0 in K0(A), where A is the C*-algebra of continuous sections of the field. We give a complete list of the Kirchberg algebras D satisfying the UCT and having finitely generated K-theory groups for which every unital separable continuous field over X with fibers isomorphic to D is automatically locally trivial or trivial. In a more general context, we show that a separable unital continuous field over X with fibers isomorphic to a KK-semiprojective Kirchberg C*-algebra is trivial if and only if it satisfies a K-theoretical Fell type condition. 相似文献
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M. Cuntz 《Journal of Combinatorial Theory, Series A》2011,118(4):1350-1363
We extend the classification of finite Weyl groupoids of rank two. Then we generalize these Weyl groupoids to ‘reflection groupoids’ by admitting non-integral entries of the Cartan matrices. This leads to the unexpected observation that the spectrum of the cluster algebra of type An−3 completely describes the set of finite reflection groupoids of rank two with 2n objects. 相似文献
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Astrid an Huef 《Journal of Functional Analysis》2011,260(5):1543-1581
We generalise the Dixmier-Douady classification of continuous-trace C?-algebras to Fell algebras. To do so, we show that C?-diagonals in Fell algebras are precisely abelian subalgebras with the extension property, and use this to prove that every Fell algebra is Morita equivalent to one containing a diagonal subalgebra. We then use the machinery of twisted groupoid C?-algebras and equivariant sheaf cohomology to define an analogue of the Dixmier-Douady invariant for Fell algebras, and to prove our classification theorem. 相似文献
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M. Burgos A.C. Márquez-García A. Morales-Campoy 《Linear algebra and its applications》2012,437(5):1183-1193
Let A and B be Banach algebras. Assume that A is unital. We prove that an additive map strongly preserves Drazin (or equivalently group) invertibility, if and only if T is a Jordan triple homomorphism. When A and B are C1-algebras, we characterize the linear maps strongly preserving generalized invertibility (in the Jordan systems’ sense), and as consequence we determine the structure of selfadjoint linear maps strongly preserving Moore–Penrose invertibility. 相似文献
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Xiang Tang 《Geometric And Functional Analysis》2006,16(3):731-766
We introduce a new kind of groupoid—a pseudo-étale groupoid, which provides many interesting examples of noncommutative Poisson
algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are the semiclassical
limits of the corresponding quantum geometries, we quantize these noncommutative Poisson algebras in the framework of deformation
quantization.
Received: September 2004 Revision: September 2005 Accepted: September 2005
Dedicated to A. Weinstein on his 60th birthday 相似文献
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S. J. Bhatt 《Proceedings Mathematical Sciences》2001,111(1):65-94
UniversalC*-algebrasC*(A) exist for certain topological *-algebras called algebras with aC*-enveloping algebra. A Frechet *-algebraA has aC*-enveloping algebra if and only if every operator representation ofA mapsA into bounded operators. This is proved by showing that every unbounded operator representation π, continuous in the uniform
topology, of a topological *-algebraA, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through
the enveloping pro-C*-algebraE(A) ofA. Given aC*-dynamical system (G,A,α), any topological *-algebraB containingC
c
(G,A) as a dense *-subalgebra and contained in the crossed productC*-algebraC*(G,A,α) satisfiesE(B) =C*(G,A,α). IfG = ℝ, ifB is an α-invariant dense Frechet *-subalgebra ofA such thatE(B) =A, and if the action α onB ism-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS(ℝ,B,α) satisfiesE(S(ℝ,B,α)) =C*(ℝ,A,α). WhenG is a Lie group, theC
∞-elementsC
∞(A), the analytic elementsC
ω(A) as well as the entire analytic elementsC
є(A) carry natural topologies making them algebras with aC*-enveloping algebra. Given a non-unitalC*-algebraA, an inductive system of idealsI
α is constructed satisfyingA =C*-ind limI
α; and the locally convex inductive limit ind limI
α is anm-convex algebra with theC*-enveloping algebraA and containing the Pedersen idealK
a
ofA. Given generatorsG with weakly Banach admissible relationsR, we construct universal topological *-algebraA(G, R) and show that it has aC*-enveloping algebra if and only if (G, R) isC*-admissible. 相似文献
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R. C. Smith 《Czechoslovak Mathematical Journal》2009,59(2):285-286
In this brief note, we see that if A is a proper uniform algebra on a compact Hausdorff space X, then A is flat.
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In this paper, we study the problem of when the corona algebra of a non-unital C*-algebra is purely infinite. A complete answer
is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result
relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the
algebra, and to the behaviour of corona projections, despite the fact that there is no real rank zero condition. 相似文献
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We prove that every noetherian affine PI Hopf algebra has finite injective dimension, which answers a question of Brown (1998).
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Esko Turunen 《Mathematical Logic Quarterly》2007,53(2):170-175
Generalizations of Boolean elements of a BL‐algebra L are studied. By utilizing the MV‐center MV(L) of L, it is reproved that an element x ∈ L is Boolean iff x ∨ x * = 1 . L is called semi‐Boolean if for all x ∈ L, x * is Boolean. An MV‐algebra L is semi‐Boolean iff L is a Boolean algebra. A BL‐algebra L is semi‐Boolean iff L is an SBL‐algebra. A BL‐algebra L is called hyper‐Archimedean if for all x ∈ L, xn is Boolean for some finite n ≥ 1. It is proved that hyper‐Archimedean BL‐algebras are MV‐algebras. The study has application in mathematical fuzzy logics whose Lindenbaum algebras are MV‐algebras or BL‐algebras. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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L.M. Camacho E.M. Cañete J.R. Gómez B.A. Omirov 《Linear and Multilinear Algebra》2013,61(9):1039-1058
In this article we present the classification of the 3-filiform Leibniz algebras of maximum length, whose associated naturally graded algebras are Lie algebras. Our main tools are a previous existence result by Cabezas and Pastor [J.M. Cabezas and E. Pastor, Naturally graded p-filiform Lie algebras in arbitrary finite dimension, J. Lie Theory 15 (2005), pp. 379–391] and the construction of appropriate homogeneous bases in the connected gradation considered. This is a continuation of the work done in Ref. [J.M. Cabezas, L.M. Camacho, and I.M. Rodríguez, On filiform and 2-filiform Leibniz algebras of maximum length, J. Lie Theory 18 (2008), pp. 335–350]. 相似文献
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不可分素C^k—代数与本原C^*—代数的讨论 总被引:2,自引:0,他引:2
本文证明:若A是不可分的素C^*-代数,且包含非0的Liminal遗传C^*-子代数,则A是本原C^*-代数,本文还给出了I型C^*-代数为本原C^*-代数的充要条件。 相似文献
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Farkhad Nematjonovich Arzikulov Shavkat Abdullayevich Ayupov 《Algebras and Representation Theory》2013,16(1):289-301
In the given article, enveloping C*-algebras of AJW-algebras are considered. Conditions are given, when the enveloping C*-algebra of an AJW-algebra is an AW*-algebra, and corresponding theorems are proved. In particular, we proved that if $\mathcal{A}$ is a real AW*-algebra, $\mathcal{A}_{sa}$ is the JC-algebra of all self-adjoint elements of $\mathcal{A}$ , $\mathcal{A}+i\mathcal{A}$ is an AW*-algebra and $\mathcal{A}\cap i\mathcal{A} = \{0\}$ then the enveloping C*-algebra $C^*(\mathcal{A}_{sa})$ of the JC-algebra $\mathcal{A}_{sa}$ is an AW*-algebra. Moreover, if $\mathcal{A}+i\mathcal{A}$ does not have nonzero direct summands of type I2, then $C^*(\mathcal{A}_{sa})$ coincides with the algebra $\mathcal{A}+i\mathcal{A}$ , i.e. $C^*(\mathcal{A}_{sa})= \mathcal{A}+i\mathcal{A}$ . 相似文献
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《Journal of Pure and Applied Algebra》2023,227(3):107206
The notion of axial algebra is closely related to 3-transposition groups, the Monster group and vertex operator algebras. In this work we continue our previous works and complete the proof that all algebras generated by a set of primitive axes not necessarily of the same type (see the definition in the body of the paper), are primitive axial algebras of Jordan type. 相似文献