共查询到20条相似文献,搜索用时 31 毫秒
1.
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
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.
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
4.
Philippe Gille 《K-Theory》2000,21(1):57-100
Let G/F be a semisimple algebraic group defined over a field F with characteristic
. Let us denote by
the Galois cohomology group introduced by Kato. If
, we show that the p-primary part of Rost's invariant
lifts in characteristic 0. This result allows to deduce properties of the Rost invariant in positive characteristic from known properties in characteristic 0. The case of Merkurjev–Suslin's invariant is specially interesting, i.e. if G/F=SL(D) for a central simple algebra D/F with degree p and class
, one has
and an element
is a reduced norm if and only if the cup-product
is trivial in
; one characterizes also in positive characteristic fields with p-dimension
by the surjectivity of reduced norms.In a second part, we study Rost invariants when the base field is complete for a discrete valuation. As planned by Serre, invariants are then linked with Bruhat–Tits' theory, this yields a new proof of their nontriviality. 相似文献
5.
Sjoerd E. Crans 《K-Theory》2003,28(1):39-105
Let
be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor
, i.e., a functor 2
q
, induce a right q-transfor
, i.e., a functor
More generally, does a functor
induce a functor
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a q-transfor
, for appropriate k-arrows
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a (q + k + 1)-transfor
, for appropriate k-arrows
I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and for n up to 5 in some cases that do not need all data and axioms of n-dimensional teisi.I apply the above to compositions in teisi, in particular to braidings and syllepses. One of the results is that a braiding on a monoidal 2-category induces a pseudo-natural transformation
, where
is the reverse of ? –, which is almost, but not quite, equal to – ?. However, in higher dimensions need not be reversible, so a braiding on a higher-dimensional tas can not be seen as a transfor A B B A. 相似文献
6.
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
7.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献
8.
B. N. Cooperstein 《Designs, Codes and Cryptography》2001,23(2):185-196
The projective plane
is embedded as a variety of projective points
in
, where M is a nine dimensional
-module for the groupG=GL(3,q
2). The hyperplane sections of thisvariety and their stabilizers in the group G aredetermined. When q 2 (mod 3) one such hyperplanesection is a member of the family of Kantor's unitary ovoids.We furtherdetermine all sections
whereD has codimension two in M and demonstratethat these are never empty. Consequences are drawn for Kantor'sovoids. 相似文献
9.
We consider the semi-group Ext(A, B) of extensions of a separable C
*-algebra A by a stable C
*-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semi-group contains the group Ext–1/2(A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext–1/2(A, B) is homotopy invariant and that it coincides with the functor of homotopy classes of asymptotic homomorphisms from C
A to M(B) that map S
A
C(
)
A into B. 相似文献
10.
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
11.
Amnon Neeman 《K-Theory》2001,22(1-2):1-144
Let
be a triangulated category, and assume it admits at least one model. In this article, we define a K-theory for
. The main theorem is that, given any bounded i-structure on
, the K-theory of the heart agrees with the K-theory of
. An immediate consequence tells us that, if two Abelian categories occur as hearts of a triangulated category for two different t-structures, then their K-theories must be isomorphic.The proof was also sketched in previous articles in this series. The virtue of this article is in the careful detail in which it is written down. 相似文献
12.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
13.
Ulrich Bunke 《K-Theory》2002,25(1):51-58
For a smooth manifold M, J. Lott has defined a secondary K-group
of local systems of R-modules, where R is some ring with a fixed representation
. If
is a smooth fibre bundle with closed fibres, then he further defines a push-forward
. In the present note, using results of X. Ma, we verify that this push-forward is functorial under iterated fibre bundles. 相似文献
14.
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
15.
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
16.
We formulate a version of the Baum–Connes conjecture for a discrete quantum group, building on our earlier work. Given such a quantum group
, we construct a directed family
-algebras (F varying over some suitable index set), borrowing the ideas of Cuntz such that there is a natural action of
satisfying the assumptions of Goswami and Kuku which makes it possible to define the analytical assembly map, say
, i= 0, 1, as in our previous work, from the
-equivariant K-homolgy groups of
to the K-theory groups of the reduced dual
(c.f. [9] and the references therein for more details). As a result, we can define the Baum–Connes maps
, and in the classical case, i.e. when
for a discrete group, the isomorphism of the above maps for i= 0, 1 is equivalent to the Baum–Connes conjecture. Furthermore, we verify its truth for an arbitrary finite-dimensional quantum group and obtain partial results for the dual of
(2). 相似文献
17.
ALAIN HÉNAUT 《Geometriae Dedicata》1997,65(1):89-101
A d-web in (
,0) is given by d complex analytic foliations of codimension one in (
,0) which are in general position. A d-web
in (
,0) is linear if all the leaves are (pieces of) hyperplanes in
and
is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in
of degree d. We characterize linear webs in (
,0). We give explicit conditions under which a linear d-web in (
,0) is algebraic and we obtain equations for
in this case. Some related problems are discussed and some questions are posed. 相似文献
18.
D. I. Panyushev 《Functional Analysis and Its Applications》2004,38(1):38-44
Let
be a reductive Lie algebra over an algebraically closed field of characteristic zero and
an arbitrary
-grading. We consider the variety
, which is called the commuting variety associated with the
-grading. Earlier it was proved by the author that
is irreducible, if the
-grading is of maximal rank. Now we show that
is irreducible for
and (E6,F4). In the case of symmetric pairs of rank one, we show that the number of irreducible components of
is equal to that of nonzero non--regular nilpotent G
0-orbits in
. We also discuss a general problem of the irreducibility of commuting varieties. 相似文献
19.
V. Yu. Popov 《Algebra and Logic》2001,40(1):55-66
It is proved that there exists an infinite sequence of finitely based semigroup varieties
such that, for all i, an equational theory for
and for the class
of all finite semigroups in
is undecidable while an equational theory for
and for the class
of all finite semigroups in
is decidable. An infinite sequence of finitely based semigroup varieties
is constructed so that, for all i, an equational theory for
and for the class
of all finite semigroups in
is decidable whicle an equational theory for
and for the class
of all finite semigroups in
is not. 相似文献
20.
Let
be an entire function of finite type with respect to finite order
and let
be a subset of an open cone in a certain n-dimensional subspace
(the smaller
, the sparser
). We assume that this cone contains a ray
0} \right\}$$
" align="middle" border="0">
. It is shown that the radial indicator
of
at any point
may be evaluated in terms of function values at points of the discrete subset
. Moreover, if
tends to zero fast enough as
over
, then this function vanishes identically. To prove these results, a special approximation technique is developed. In the last part of the paper, it is proved that, under certain conditions on
and
, which are close to exact conditions, the function
bounded on
is bounded on the ray. 相似文献