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1.
V. M. Petrogradsky 《Israel Journal of Mathematics》1999,113(1):323-339
Suppose that
% MathType!End!2!1! is a variety of Lie algebras, and letc
n(
% MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF(
% MathType!End!2!1!,X) of the variety
% MathType!End!2!1!. We consider an exponential generating function
% MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided
the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms
of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety.
Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands.
The main observation here is thatC(
% MathType!End!2!1!),z) behaves like a composition of three functionsC(
% MathType!End!2!1!),z), exp(z), andC(
% MathType!End!2!1!),z).
Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where
he was DAAD-fellow. 相似文献
2.
Let
% MathType!End!2!1! be the three-fold cover of SL2. We prove there is a lifting of the genuine automorphic representations of
% MathType!End!2!1! to the automorphic representations of SL2, using a relative trace formula.
Partially supported by NSF DMS 9304580.
Partially supported by NSF DMS 7209098. 相似文献
3.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
4.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
– | • is finitely generated and infinite-dimensional, but has only finitedimensional quotients; |
– | • has a subalgebra of finite codimension, isomorphic toM 2(k); |
– | • is prime; |
– | • has quadratic growth, and therefore Gelfand-Kirillov dimension 2; |
– | • is recursively presented; |
– | • satisfies no identity; |
– | • contains a transcendental, invertible element; |
– | • is semiprimitive if % MathType!End!2!1! has characteristic ≠2; |
– | • is graded if % MathType!End!2!1! has characteristic 2; |
– | • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!; |
– | • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!. |
5.
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
6.
For a given centred convex bodyK of ℝ,n≥3, let
be the class of all convex bodies with the same projection body asK. The question whetherK can be expressed as a Blaschke average of two non-homothetic bodies from
is considered. Necessary and sufficient conditions onK to be Blaschke decomposable in
are given.
The paper provides also a characterization of the bodiesK such that the Blaschke indecomposable bodies in
are dense in
itself. 相似文献
7.
Let
denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let
be the class of multipliers for
, i.e. ergodic transformations whose all ergodic joinings with any element of
are also in
. Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of
. Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations.
Dedicated to Hillel Furstenberg on the occasion of his retirement
The first-named author was supported in part by CRDF, grant UM1-2546-KH-03.
The second-named author was supported in part by KBN grant 1P03A 03826. 相似文献
8.
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
9.
V. Hinich 《Israel Journal of Mathematics》1991,73(3):297-308
Let
be a nilpotent orbit of the adjoint action of a complex connected semi-simple Lie group on its Lie algebra. We prove that
the normalization of the closure of
is Gorenstein and has rational singularities. 相似文献
10.
It is known [KRS] that for each finitely generated Banach algebra
there exists a numberN such that for eachn>N the matrix algebras
can be generated by three idempotents. In this paper we show that the same statement is true for direct sums
and
, where
is a finitely generated free algebra, i.e. polynomials in several non-commuting variables. These results are new even for
algebras
because the numberN we obtain here improves known estimates (see for example [R]). We show that the algebra
can be generated by two idempotents if and only ifn
j
=2 for eachj and
is singly generated. Also we give an example of a free singly generated algebra
for which
can not be generated by two idempotents. But% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x%
fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacuWFSeIqgaacaaaa!409A!\[{\tilde
{\cal B}}\] can be generated by three idempotents for each singly generated free algebra
. 相似文献
11.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献
12.
Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. 相似文献
13.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
14.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献
15.
Assume
% MathType!End!2!1! and let Ω⊂R
N(N≥4) be a smooth bounded domain, 0∈Ω. We study the semilinear elliptic problem:
% MathType!End!2!1!. By investigating the effect of the coefficientQ, we establish the existence of nontrivial solutions for any λ>0 and multiple positive solutions with λ,μ>0 small. 相似文献
16.
We prove that for almost allσ ∈G ℚ the field
has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→
there exists a point a ∈
such thatϕ(a) ∈ ℤr. We then say that
is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields
other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ. 相似文献
17.
We consider a Skorohod map
which takes paths in
to paths which stay in the positive orthant
. We let
be the domain of definition of
. A convex and lower semi-continuous function
and a set
are given. We are concerned with the calculation of the infimum of the value
for t ⩾ 0 and absolutely continuous
subject to the conditions
and
. We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state
distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems.
This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for
its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations
of heavily loaded queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
We study pro-‘finite dimensional finite exponent’ completions of restricted Lie algebras over finite fields of characteristicp. These compact Hausdorff topological restricted Lie algebras, called pro-
restricted Lie algebras, are the restricted Lie-theoretic analogues of pro-p groups. A structure theory for pro-
restricted Lie algebras with finite rank is developed. In particular, the centre of such a Lie algebra is shown to be open.
As an application we examinep-adic analytic pro-p groups in terms of their associated pro-
restricted Lie algebras.
Supported by NSERC of Canada. 相似文献
19.
Let
and
the foliations by the null geodesics of some lorentzian metricg on the torus
. We analyse how geodesic completeness properties ofg are related to the dynamics of
and
. 相似文献
20.
There are exactlytwo non-equivalent [32,11,12]-codes in the binaryReed-Muller code
which contain
and have the weight set {0,12,16,20,32}. Alternatively,the 4-spaces in the projective space
over the vector space
for which all points have rank 4 fall into exactlytwo orbits under the natural action of PGL(5) on
. 相似文献