共查询到20条相似文献,搜索用时 11 毫秒
1.
We prove the Farrell-Jones Conjecture for the algebraic -theory of a group ring in the case where the group is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The coefficient ring is an arbitrary associative ring with unit and the result applies to all dimensions.
2.
A. S. Merkurjev 《K-Theory》1993,7(1):1-3
We prove that the generic element inSK
1(D) for a simple algebraD of the index divisible by 4 is nontrivial. It implies that the variety of an algebraic group SL(1,D) is not rational. 相似文献
3.
Stephen Allen David Pask Aidan Sims 《Proceedings of the American Mathematical Society》2006,134(2):455-464
Given a -graph and an element of , we define the dual -graph, . We show that when is row-finite and has no sources, the -algebras and coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the -theory of when is finite and strongly connected and satisfies the aperiodicity condition.
4.
M. Hemdaoui 《Rendiconti del Circolo Matematico di Palermo》2000,49(3):435-444
Dans cette note, nous montrons qu’il est possible d’étendre le théorème de factorisation de Weierstrass pour certains éléments
d’une algèbre de BanachA. 相似文献
5.
Let be an algebraic type. To each classK of -algebras a consequence relation
K
defined on the set of -equations is assigned. Some weak forms of the deduction theorem for
K
and their algebraic counterparts are investigated. The (relative) congruence extension property (CEP) and its variants are discussed.CEP is shown to be equivalent to a parameter-free form of the deduction theorem for the consequence
K
.CEP has a strong impact on the structure ofK: for many quasivarietiesK,CEP implies thatK is actually a variety. This phenomenon is thoroughly discussed in Section 5. We also discuss first-order definability of relative principal congruences. This property is equivalent to the fact that the deduction theorem for
K
is determined by a finite family of finite sets of equations. The following quasivarietal generalization of McKenzie's [26] finite basis theorem is proved:LetK be quasivariety of algebras of finite type in which the principalK-congruences are definable. ThenK is finitely axiomatizable iff either the classK
FSI
(of all relatively finitely subdirectly irreducible members ofK) or the class KSI (of all relatively subdirectly irreducible members ofK) is strictly elementary.Applications of the theory to Heyting, interior, Sugihara, and ukasiewicz algebras are provided.Presented by R. McKenzie.The paper was presented in a talk given to the Conference on Algebraic Logic, Budapest, August 1988. 相似文献
6.
Allan J. Silberger 《Transactions of the American Mathematical Society》1996,348(11):4673-4686
Let be a reductive -adic group. In his paper, ``The Plancherel Formula for Reductive -adic Groups", Harish-Chandra summarized the theory underlying the Plancherel formula for and sketched a proof of the Plancherel theorem for . One step in the proof, stated as Theorem 11 in Harish-Chandra's paper, has seemed an elusively difficult step for the reader to supply. In this paper we prove the Plancherel theorem, essentially, by proving a special case of Theorem 11. We close by deriving a version of Theorem 11 from the Plancherel theorem.
7.
Stephen D. Theriault 《Transactions of the American Mathematical Society》2007,359(9):4511-4535
A compact, connected, simple Lie group localized at an odd prime is shown to be homotopy equivalent to a product of homotopy associative, homotopy commutative spaces, provided the rank of is low. This holds for , for example, if . The homotopy equivalence is usually just as spaces, not multiplicative spaces. Nevertheless, the strong multiplicative features of the factors can be used to prove useful properties, which after looping can be transferred multiplicatively to . This is applied to prove useful information about the torsion in the homotopy groups of , including an upper bound on its exponent.
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12.
We prove an apparently new type of ergodic theorem, and apply it to the site percolation problem on sparse random sublattices of Zd (d≥2), called “lattices with large holes”. We show that for every such lattice the critical probability lies strictly between zero and one, and the number of the infinite clusters is at most two with probability one. Moreover for almost every such lattice, the infinite cluster, if it exists, is unique with probability one. 相似文献
13.
This paper presents an explicit relation between the two sets which are well-known generators of the center of the universal enveloping algebra of the Lie algebra : one by Capelli (1890) and the other by Gelfand (1950). Our formula is motivated to give an exact analogy for the classical Newton's formula connecting the elementary symmetric functions and the power sum symmetric functions. The formula itself can be deduced from a more general result on Yangians obtained by Nazarov. Our proof is elementary and has an advantage in its direct accessibility.
14.
We present a new and constructive proof of the Peter‐Weyl theorem on the representations of compact groups. We use the Gelfand representation theorem for commutative C*‐algebras to give a proof which may be seen as a direct generalization of Burnside's algorithm [3]. This algorithm computes the characters of a finite group. We use this proof as a basis for a constructive proof in the style of Bishop. In fact, the present theory of compact groups may be seen as a natural continuation in the line of Bishop's work on locally compact, but Abelian, groups [2]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
E. V. Troitsky 《Functional Analysis and Its Applications》2006,40(2):117-125
The paper consists of two parts. In the first part, we prove a noncommutative analog of the Riesz(— Markov—Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the underlying space. In the second part, using this result, we prove a weak version of a Burnside type theorem on twisted conjugacy for arbitrary discrete groups. 相似文献
16.
Tianxuan Miao 《Transactions of the American Mathematical Society》1999,351(11):4675-4692
For any locally compact group , let and be the Fourier and the Fourier-Stieltjes algebras of , respectively. is decomposed as a direct sum of and , where is a subspace of consisting of all elements that satisfy the property: for any and any compact subset , there is an with and such that is characterized by the following: an element is in if and only if, for any there is a compact subset such that for all with and . Note that we do not assume the amenability of . Consequently, we have for all if is noncompact. We will apply this characterization of to investigate the general properties of and we will see that is not a subalgebra of even for abelian locally compact groups. If is an amenable locally compact group, then is the subspace of consisting of all elements with the property that for any compact subset , .
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18.
D'Alembert's proof of the fundamental theorem of algebra 总被引:1,自引:0,他引:1
D'Alembert's proof of the fundamental theorem of algebra (FTA), the first published, is still widely misunderstood. Typical of d'Alembert, his work is bold and imaginative but in need of significant repair. The proof is examined in detail, in both the 1746 and 1754 versions, along with commentary over 250 years and recent efforts to revive d'Alembert's reputation. A particular challenge is to work with algebraic equations while avoiding dependence on the FTA itself. A repaired version is offered. 相似文献
19.
Ryszard Jajte 《Proceedings of the American Mathematical Society》2004,132(8):2475-2481
Using simple techniques of finite von Neumann algebras, we prove a limit theorem for random matrices.
20.
Dae-Woong LEE 《数学年刊B辑(英文版)》2016,37(6):951-962
Given a connected CW-space X, SN T(X) denotes the set of all homotopy types[X′] such that the Postnikov approximations X~((n)) and X′~((n)) are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy ntypes of the suspension of the wedges of the Eilenberg-MacL ane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT(Σ(K(Z, 2a_1) ∨ K(Z, 2a_2) ∨···∨ K(Z, 2a_k))) = * for a_1 a_2 ··· a_k, as a far more general conjecture than the original one of the same n-type posed by McG ibbon and M?ller(in [McG ibbon, C. A. and M?ller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285–293].) 相似文献