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1.
H. E. A. Campbell I. Hughes F. Pappalardi P. S. Selick 《Commentarii Mathematici Helvetici》1991,66(1):322-331
In [1] the first and last authors studied a decomposition ofH
*(R
P
∞×…×R
P
∞;F
2) into modules over the Steenrod algebra obtained from an action of the cyclic group
. Here a minimal set of generators for the ring of invariants is characterized and counted by analyzing the associated ring
of Laurent polynomials. A structure theorem for the ring of invariant Laurent polynomials is given and a ‘destabilisation
cancels localisation’ theorem is obtained.
The authors gratefully acknowledge the support of NSERC. 1980 Mathematics Subject classification, 13F20, 55. Keywords: Invariant
theory, Steenrod algebra. 相似文献
2.
Summary LetG be the coadjoint group of a finite-dimensional complex Lie algebrag. Forg solvable, the Dixmier-map is known to be a homeomorphism
of the orbit space
/G onto the space χ of primitive ideals in the enveloping algebra U(G) [6,15]. For
, the Dixmier-map is known to be a bijection (and in general not a homeomorphism)
with the space χl of all completely prime primitive ideals [7, 16]. Here we derive from a result ofW. SOERGEL [18], that this map issheet- wise a homeomorphism onto the image. Here a sheet is a maximal irreducible subset consisting of orbits of a fixed dimension; obviouslyg decomposes into finitely many sheets [3]. The results of this paper hold more generally forg semisimple, if one restricts to a sheet of polarizable orbits, where a Dixmier-map can be defined.
Relative to a fixed polarization (a parabolic subalgebra)p ⊂g let I be the annihilator of the generic module induced from p. The „relative enveloping algebra“
) has been studied e.g. bySOERGEL [19, 18]. Its center Z is described here by a relative Harish-Chandra isomorphism of the normalization
with a suitable ring of group invariants (3.2). We study here the extension
ofU by
. We suggest that this very mild central extension ofU generates good properties and is very suitable for the study of the Dixmier-map (cf.4.3,5.6).
In particular, we conjecture in case
: Every minimal primitive ideal of
is generated by a maximal ideal of the center. This would generalize for
a well known theorem ofM. Duflo (casep Borel, where
).
AsJ. Dixmier communicated in a letter, the main result here is exactly what he had hoped for when he first introduced a notion of sheets
many years ago.
Added in proof: This conjecture will be proved in a subsequent paper. 相似文献
Added in proof: This conjecture will be proved in a subsequent paper. 相似文献
3.
Feng WEI 《数学学报(英文版)》2005,21(4):823-832
Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф(Xi^△j) is a reduced generalized differential identity for an essential ideal of R, then ф(Zije(△j )) is a generalized polynomial identity for RF, where e(△j) are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф(Xi△j) is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф(Zij) is a generalized polynomial identity for [R, R]. Moreover, if ф(Xi△j) is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф(Zij) is a generalized polynomial identity for Q. 相似文献
4.
任立顺 《高校应用数学学报(英文版)》2003,18(2):138-142
§ 1 IntroductionThe deformations of an elastic beam are described by a fourth-order two-pointbound-ary value problem[1 ] .The boundary conditions are given according to the controls at theends of the beam. For example,the nonlinear fourth order problemu(4) (x) =λa(x) f(u(x) ) ,u(0 ) =u′(0 ) =u′(1 ) =u (1 ) =0 (1 .1 ) λdescribes the deformations of an elastic beam whose one end fixed and the other slidingclamped.The existence of solutions of (1 .1 ) λhas been studied by Gupta[1 ] . But … 相似文献
5.
刘斌 《高校应用数学学报(英文版)》2002,17(2):135-144
§ 1 IntroductionWe are interested in the existence ofthree-solutions ofthe following second-order dif-ferential equations with nonlinear boundary value conditionsx″=f( t,x,x′) , t∈ [a,b] ,( 1 .1 )g1 ( x( a) ,x′( a) ) =0 , g2 ( x( b) ,x′( b) ) =0 ,( 1 .2 )where f:[a,b]×R1 ×R1 →R1 ,gi:R1 ×R1 →R1 ( i=1 ,2 ) are continuous functions.The study ofthe existence of three-solutions ofboundary value prolems forsecond or-der differential equations was initiated by Amann[1 ] .In[1 … 相似文献
6.
The pointset E of an absolute plane
can be provided with a binary operation "+" such that (E, +) becomes a loop and for each a
E \ {o} the line [a] through o and a is a commutative subgroup of (E, +). Two elements a, b
E \ {o} are called independent if [a] ∩ [b] = {o} and the absolute plane is called vectorspacelike if for any two independent elements we have E = [a] + [b] := {x + y | x
[a], y
[b]}. If
is singular then (E, +) is a commutative group and
is vectorspacelike iff
is Euclidean. If
is a hyperbolic plane then
is vectorspacelike and in the continous case if a, b are independent, each point p has a unique representation as a quasilinear combination p = α · a + μ · b where α · a
[a]and β · b
[b] are points, α, β real numbers such that λ (o, λ · a) = |λ|· λ (o, a) and λ (o, μ · b) = |μ|. λ(o, b) and λ is the distance function.
This work was partially supported by the Research Project of MIUR (Italian Ministery of Education and University) “Geometria
combinatoria e sue applicazioni” and by the research group GNSAGA of INDAM.
Dedicated to Walter Benz on the occasion of his 75
th
birthday, in friendship 相似文献
7.
Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn(R) the ring of all n x n matrices over R. Let (Jn(R)) be the additive subgroup of Mn(R) generated additively by all idempotent matrices. Let JJ = (Jn(R)) or Mn(R). We describe the additive preservers of idempotence from JJ to Mm(R) when 2 is a unit of R. Thereby, we also characterize the Jordan (respectively, ring and ring anti-) homomorphisms from Mn (R) to Mm (R) when 2 is a unit of R. 相似文献
8.
Hüseyin Bor 《Proceedings Mathematical Sciences》1994,104(2):367-372
In this paper using δ-quasi-monotone sequences a theorem on
summability factors of infinite series, which generalizes a theorem of Bor [4] on
summability factors of infinite series, is proved. Also, in the special case this theorem includes a result of Mazhar [8]
on |C, 1|k summability factors. 相似文献
9.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
10.
In this note, the authors prove that the commutator generated by θ-type Calderón-Zygmund operator T and a Lipschitz function is bounded from L
p
(R
n
) into (R
n
) and also maps from (R
n
) into BMO (R
n
).
Supported by NSFC(10571014), NSFC(10571156), the Doctor Foundation of Jxnu (2443), the Natural Science Foundation of Jiangxi
province(2008GZS0051). 相似文献
11.
Nuria Corral 《Bulletin of the Brazilian Mathematical Society》2009,40(2):181-224
The polar curves of foliations having a curve C of separatrices generalize the classical polar curves associated to hamiltonian foliations of C. As in the classical theory, the equisingularity type ℘() of a generic polar curve depends on the analytical type of , and hence of C. In this paper we find the equisingularity types ε(C) of C, that we call kind singularities, such that ℘() is completely determined by ε(C) for Zariski-general foliations . Our proofs are mainly based on the adjunction properties of the polar curves. The foliation-like framework is necessary,
otherwise we do not get the right concept of general foliation in Zariski sense and, as we show by examples, the hamiltonian
case can be out of the set of general foliations.
The author was partially supported by the research projects MTM2007-66262 (Ministerio de Educación y Ciencia), MTM2006-15338-C02-02
(Ministerio de Educación y Ciencia),VA059A07 (Junta de Castilla y León) and PGIDITI06PXIB377128PR (Xunta de Galicia). 相似文献
12.
We consider the problem of the identification of continuous functionsf∶[0, 1]→R, by means of the sums
. This is not possible, in general, but we prove that it may be the case under auxiliary conditions. We also study the behaviour
of a well known exceptional function.
Sunto Consideriamo il problema dell’identificazione delle funzioni continuef:[0,1]→ →R, mediante le somme . Ciò non è, in generale, possibile: dimostriamo però tale possibilità sotto condizioni ausiliarie. Studiamo inoltre il comportamento di una ben nota funzione eccezionale.相似文献
13.
Koji Matsumoto Gabriel Teodor Pripoae 《Rendiconti del Circolo Matematico di Palermo》2003,52(3):351-366
We consider a family of left invariant semi- Riemannian metrics on some extension of the Heisenberg group by the real line
(denoted by
). We find a 3-dimensional foliation, which is minimal but not totally geodesic with respect to all the metrics of this family.
Other two 3-dimensional totally geodesic (isometric) foliations on
are determined.
We consider also a non-holonomic 3-dimensional distribution, admitting integral surfaces which are totally geodesic in the
ambiant space
. Two of them are isomorphic with the two-dimensional non-commutative Lie group (which is not totally geodesic in the additive
Lie groupR
4!).
Following the different possible choices of the signatures of the metrics and the sign of the parameters, we put in evidence
twelve new classes of invariant spacetime structures onR
4, together with their energy-momenta. 相似文献
14.
We prove the following theorem. Assume f ∈ L
∞(R
2) with bounded support. If f is continuous at some point (x
1,x
2) ∈ R
2, then the double Fourier integral of f is strongly q-Cesàro summable at (x
1,x
2) to the function value f(x
1,x
2) for every 0 < q < ∞. Furthermore, if f is continuous on some open subset
of R
2, then the strong q-Cesàro summability of the double Fourier integral of f is locally uniform on
.
Research partially supported by the Australian Research Council and the Hungarian National Foundation for Scientific Research
under Grant T 046 192. 相似文献
15.
Let R(D) be the algebra generated in Sobolev space W22(D) by the rational functions with poles outside the unit disk D. In this paper the multiplication operators Mg on R(D) is studied and it is proved that Mg ~ Mzn if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then Mg has uncountably many Banach reducing subspaces if and only if n > 1. 相似文献
16.
Corrado Tanasi 《Rendiconti del Circolo Matematico di Palermo》1985,34(2):300-309
In this sequel to our previous paper [2] we show that on a surfacesS of genusg>1, the arational measured foliations are generic inM F. We also show that ergodic measured foliations are necessarily non-rational (i.e. without closed leaves). 相似文献
17.
We can consider the Riemann-Stieltjes integral dg as an integral of a point function f with respect to an interval function g. We could extend it to the Henstock-Stieltjes integral. In this paper, we extend it to a generalized Stieltjes integral dg of a point function f with respect to a function g of divisions of an interval. Then we prove for this integral the standard results in the theory of integration, including
the controlled convergence theorem.
相似文献
18.
G. Androulakis P. Dodos G. Sirotkin V. G. Troitsky 《Israel Journal of Mathematics》2009,169(1):221-250
V. D. Milman proved in [20] that the product of two strictly singular operators on L
p
[0, 1] (1 ⩽ p < 1) or on C[0, 1] is compact. In this note we utilize Schreier families in order to define the class of -strictly singular operators, and then we refine the technique of Milman to show that certain products of operators from this
class are compact, under the assumption that the underlying Banach space has finitely many equivalence classes of Schreier-spreading
sequences. Finally we define the class of -hereditarily indecomposable Banach spaces and we examine the operators on them.
This project originated at SUMIRFAS conference in 2005 in Texas A&M University. The authors wish to thank the organizers of
the SUMIRFAS conference for their hospitality. 相似文献
19.
20.
According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of
-modules, theresidue complex
. These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex
is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes,
and
, which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical
dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms. 相似文献