排序方式: 共有87条查询结果,搜索用时 31 毫秒
11.
Rebekah Hahn Stephen Mitchell 《Transactions of the American Mathematical Society》2007,359(11):5207-5238
The Iwasawa algebra is a power series ring in one variable over the -adic integers. It has long been studied by number theorists in the context of -extensions of number fields. It also arises, however, as a ring of operations in -adic topological -theory. In this paper we study -local stable homotopy theory using the structure theory of modules over the Iwasawa algebra. In particular, for odd we classify -local spectra up to pseudo-equivalence (the analogue of pseudo-isomorphism for -modules) and give an Iwasawa-theoretic classification of the thick subcategories of the weakly dualizable spectra.
12.
Andrew S. Toms Wilhelm Winter 《Transactions of the American Mathematical Society》2007,359(8):3999-4029
Say that a separable, unital -algebra is strongly self-absorbing if there exists an isomorphism such that and are approximately unitarily equivalent -homomorphisms. We study this class of algebras, which includes the Cuntz algebras , , the UHF algebras of infinite type, the Jiang-Su algebra and tensor products of with UHF algebras of infinite type. Given a strongly self-absorbing -algebra we characterise when a separable -algebra absorbs tensorially (i.e., is -stable), and prove closure properties for the class of separable -stable -algebras. Finally, we compute the possible -groups and prove a number of classification results which suggest that the examples listed above are the only strongly self-absorbing -algebras.
13.
Nitu Kitchloo 《Advances in Mathematics》2009,221(4):1191-1226
We give a topological interpretation of the highest weight representations of Kac-Moody groups. Given the unitary form G of a Kac-Moody group (over C), we define a version of equivariant K-theory, KG on the category of proper G-CW complexes. We then study Kac-Moody groups of compact type in detail (see Section 2 for definitions). In particular, we show that the Grothendieck group of integrable highest weight representations of a Kac-Moody group G of compact type, maps isomorphically onto , where EG is the classifying space of proper G-actions. For the affine case, this agrees very well with recent results of Freed-Hopkins-Teleman. We also explicitly compute for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E10. 相似文献
14.
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
15.
Given a quasi-projective complex variety X and a projective variety Y, one may endow the set of morphisms, Mor(X, Y), from X to Y with the natural structure of a topological space. We introduce a convenient technique (namely, the notion of a functor on the category of 'smooth curves') for studying these function complexes and for forming continuous pairings of such. Building on this technique, we establish several results, including (1) the existence of cap and join product pairings in topological cycle theory; (2) the agreement of cup product and intersection product for topological cycle theory; (3) the agreement of the motivic cohomology cup product with morphic cohomology cup product; and (4) the Whitney sum formula for the Chern classes in morphic cohomology of vector bundles. 相似文献
16.
本文研究了连续函数代数C(X)与某个C*-代数 A的张量积C(X) A的自同构群.当 A是有单位元且具有平凡中心的C*-代数时,本文完全刻划了C(X) A的自同构群.利用AF-代数的K-理论,本文还刻划了当X是全不连通的紧致Hausdorff空间时,C(X)与紧算子理想的张量积的自同构群. 相似文献
17.
Abstract
Let A be a unital simple C*-algebra of real zero, stable rank one, with weakly unperforated K
0(
A) and unique normalized quasi-trace τ, and let X be a compact metric space. We show that two monomorphisms φ, ψ : C(X)→A are approximately unitarily equivalent if and only if φ and ψ induce the same element in KL(C(X), A) and the two lineal functionals τ∘φ and τ∘ψ are equal. We also show that, with an injectivity condition, an almost multiplicative
morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism.
Research partially supported by NSF Grants DMS 93-01082 (H.L) and DMS-9401515(G.G). This work was reported by the first named
author at West Coast Operator Algebras Seminar (Sept. 1995, Eugene, Oregon) 相似文献
18.
王立庆 《数学年刊A辑(中文版)》2001,(5)
本文讨论了关于 Waldhausen范畴的K理论与循环同调理论的联系.主要是推广了 Dennis迹映射和Jones-Goodwillie Chern映射.证明了迹映射保持各自的乘法结构.最后讨论了双变量的情形. 相似文献
19.
C*-Algebras and Controlled Topology 总被引:1,自引:0,他引:1
We describe some aspects of the relationship between the controlled topology and C*-algebra approaches to the Novikov conjecture. 相似文献
20.