共查询到20条相似文献,搜索用时 31 毫秒
1.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
2.
Let
be an
-filtered category in the sense of Karoubi. This is the categorical analogue of an ideal
in a ring
. Pedersen and Weibel constructed a fibration of K-theory spectra associated with the sequence
. We present a new easier proof based on Waldhausen' generic fibration. 相似文献
3.
Let be the set of nonnegative integers and the ring of integers. Let
be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of
yields that the subrings generated by them coincide. This subring is the sum of the ideal
consisting of all matrices in
with only a finite number of nonzero entries and the subring of
generated by the identity matrix. Regular elements are also described. We characterize all ideals of
, show that all ideals are finitely generated and that not all ideals of
are principal. Some general ring theoretic properties of
are also established. 相似文献
4.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
5.
Niels Jakob Laustsen 《K-Theory》2001,22(3):241-249
Let
Figiel's reflexive Banach space which is not isomorphic to its Cartesian square. We show that the K
0group of the algebra
of continuous, linear operators on
contain a subgroup isomorphic to the group c
00(
) of sequences
rational numbers with z
n=0 eventually. 相似文献
6.
Graeme West 《Integral Equations and Operator Theory》1995,22(3):352-359
Suppose
is a von Neumann algebra on a Hilbert space
and
is any ideal in
. We determine a topology
on
, for which the members of
that are
to norm continuous are exactly those in
; and a bornology
on
such that the elements of
which map the unit ball to an element of
, equivalently those members of
that are norm to
bounded, are exactly those in
. This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces. 相似文献
7.
We find a regular deformation retraction
n,r
(K): Idem
n,r
(K) G
n,r
(K) from the manifold Idem
n,r
(K) of idempotent n × n matrices with rank r to the Grassmannian manifold G
n,r
(K) over K the reals, complex numbers or quaternions. Then we derive an injection
from the sets of homotopy classes of complex-valued polynomial to such a set of real-valued regular maps, where
denotes the Zariski closure in the affine space
n
of a subset
n
. Furthermore, we list complex-valued polynomial maps
2
2 of any Brouwer degree and deduce that the map ()2,1: Idem()2,1 G()2,1 yields an isomorphism
[
2
]
[
2,
2] of cyclic infinite homotopy groups. Finally, we show that every nonzero even Brouwer degree of the spheres
n
and
n
cannot be realized by a real-valued (resp. complex-valued) homogeneous polynomial map provided that n is even. 相似文献
8.
For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K
*
G
(E(G,
in)), is isomorphic to K
*
G
(E(G,
)), where E(G,
) denotes the classifying space for the family of finite cyclic subgroups of G. Letting
be the family of virtually cyclic subgroups of G, we also establish that and related results. 相似文献
9.
Damjan Kobal 《K-Theory》1999,17(2):113-140
The goal of this paper is to present a new view on the link between the well known K-theory of finitely generated projective modules and much less understood K-theory of Hermitian forms on finitely generated projective modules.For a given Hermitian ring (R, , ), we obtain the K-theory space KR equipped with an involution and the Hermitian K-theory space KHerm(R, , ). The fixed subspace
2 is homotopy equivalent to the Hermitian K-theory space KHerm(R,, , ). We construct the Karoubi Tower diagram, which is obtained by iterating Karoubi's construction of the homotopy fibers of the forgetful and hyperbolic maps. Using an interesting factorization of these maps, we prove various homotopy properties of the Karoubi Tower. The homotopy inverse limit of the Karoubi Tower is homotopy equivalent to the homotopy fibre of the inclusion of the fixed set
2 into the homotopy fixed set
h
2. Considering Karoubi's fundamental periodicity theorem, the Karoubi Tower generalizes the low dimensional connections between Hermitian K-theory and K-theory groups. Illustrative examples of the Karoubi Tower are given by the finite field case and the classical Hermitian rings over
,
and
. Considering topological K-theory for these cases, the Karoubi Tower comprises the classical Bott periodicity.Another important application of the Karoubi Tower is an elegant and comprehensive generalization of the classical invariants of quadratic forms. 相似文献
10.
Michel Matthey 《K-Theory》2001,24(1):87-107
Let be a group, F the free
-module on the set of finite order elements in , with acting by conjugation, and
the ring extension of
by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaWaaiWaaeaada% WcaaqaaiaaigdaaeaatCvAUfKttLearyGqLXgBG0evaGqbciab-5ga% UbaaieaacaGFLbGaaGOmaiaabc8acqWFPbqAcaqGVaGae8NBa42aaq% qaaeaacqGHdicjcqaHZoWzcqGHiiIZcqqHtoWrcaqGGaGaae4Baiaa% bAgacaqGGaGaae4BaiaabkhacaqGKbGaaeyzaiaabkhacaqGGaGae8% NBa4gacaGLhWoaaiaawUhacaGL9baaaaa!563E!\[\left\{ {\frac{1}{n}e2{\text{\pi }}i{\text{/}}n\left| {\exists \gamma \in \Gamma {\text{ of order }}n} \right.} \right\}\]. For a ring R with
, we build an injective assembly map
, detected by the Dennis trace map. This is proved by establishing a delocalization property for the assembly map
in Hochschild homology, namely providing a gluing of simpler assembly maps (i.e. localized at the identity of ) to build
, and by delocalizing a known assembly map in K-theory to define
. We also prove the delocalization property in cyclic homology and in related theories. 相似文献
11.
Mikael R?rdam 《K-Theory》1995,9(1):31-58
A classification is given of the simple Cuntz-Krieger algebras
. It is proved that these algebras are classified up to stable isomorphism by their K0-group. Thus the sign of the determinant of 1 —A is not an isomorphism invariant. The (non-stabilized) isomorphism type of
is determined by K0(
) together with the position of the class of the unit of
. 相似文献
12.
Pierre-yves Le Gall 《K-Theory》1999,16(4):361-390
Let
be a locally compact topological groupoid, A and B two C*-algebras endowed with a continuous action of
. We define an operator K-theory group K K
(A,B). We describe two basic properties of this theory: the existence of a Kasparov product and functoriality with respect to groupoid cocycles. 相似文献
13.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
14.
The Hodge Filtration and Cyclic Homology 总被引:1,自引:0,他引:1
Charles Weibel 《K-Theory》1997,12(2):145-164
We relate the Hodge filtration of the cohomology of a complex algebraic variety X to the Hodge decomposition of its cyclic homology. If X is smooth and projective,
is the quotient of the Betti cohomology
by the
piece of the Hodge filtration. 相似文献
15.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
16.
17.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
18.
Renate Jaritz 《Geometriae Dedicata》1997,64(3):365-372
An ordered plane is an incidence structure (
) with an order function , which satisfies the axioms (G), (V) and (S), but no continuation--axiom is required. Points a, b E are said to be in distinct sides of a line
iff
and in the same side if
, respectively. For any lines
,
and
we prove that if b,c are in the same side of line A and a,c are in the same side of B , then a and b are in distinct sides of C. As conclusions we deduce that is harmonic and that in each complete quadrangle the intersection points of the diagonals are never collinear, which is known as the axiom of Fano. So the Fano-axiom holds in each ordered plane, and also in those with boundary points. 相似文献
19.
Natalie M. Priebe 《Geometriae Dedicata》2000,79(3):239-265
In this paper, a technique for analyzing levels of hierarchy in a tiling
of Euclidean space is presented. Fixing a central configuration P of tiles in
, a `derived Voronoï' tessellation
P is constructed based on the locations of copies of P in
. A family of derived Voronoï tilings
is formed by allowing the central configurations to vary through an infinite number of possibilities. The family
will normally be an infinite one, but we show that for a self-similar tiling
it is finite up to similarity. In addition, we show that if the family
is finite up to similarity, then
is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided. 相似文献
20.
A. I. Budkin 《Algebra and Logic》2005,44(4):213-218
Let qG be a quasivariety generated by a group G and
be a non-Abelian quasivariety of groups with a finite lattice of subquasivarieties. Suppose
is contained in a quasivariety generated by the following two groups: a free 2-nilpotent group F2(
2) of rank 2 and a free metabelian (i.e., with an Abelian commutant) group F2(
2) of rank 2. It is proved that either
= qF2(
2) or
= qF2(
2) in this instance.__________Translated from Algebra i Logika, Vol. 44, No. 4, pp. 389–398, July–August, 2005. 相似文献