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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.
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!. |
3.
Ilijas Farah 《Israel Journal of Mathematics》2006,154(1):235-246
We prove two results about the quotient over the asymptotic density zero ideal. First, it is forcing equivalent to
% MathType!End!2!1!, where
% MathType!End!2!1! is the homogeneous probability measure algebra of characterc. Second, if it has analytic Hausdorff gaps, then they look considerably different from proviously known gaps of this form.
Partially supported by NSERC. 相似文献
4.
Let Γ = SL(n, ℤ) or any subgroup of finite index, n ≥ 4. We show that the standard action of Γ on
n is locally rigid, i.e., every action of Γ on
n by C∞ diffeomorphisms which is sufficiently close to the standard action is conjugate to the standard action by a C∞ diffeomorphism. In the course of the proof, we obtain a global rigidity result (Theorem 4.12) for actions of free abelian
subgroups of maximal rank in SL(n, ℤ).
Partially supported by NSF grant DMS9011749. 相似文献
5.
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
6.
Kyewon Koh Park 《Israel Journal of Mathematics》1999,113(1):243-267
Given aZ
2-process, the measure theoretic directional entropy function,h(
% MathType!End!2!1!), is defined on
% MathType!End!2!1!. We relate the directional entropy of aZ
2-process to itsR
2 suspension. We find a sufficient condition for the continuity of directional entropy function. In particular, this shows
that the directional entropy is continuous for aZ
2-action generated by a cellular automaton; this finally answers a question of Milnor [Mil]. We show that the unit vectors
whose directional entropy is zero form aG
δ subset ofS
1. We study examples to investigate some properties of directional entropy functions.
This research is supported in part by BSRI and KOSEF 95-0701-03-3. 相似文献
7.
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
8.
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
9.
We focus on
% MathType!End!2!1!(A), the filter of supersets ofA in the structure of the computably enumerable sets under the inclusion relation, whereA is an atomlessr-maximal set. We answer a long-standing question by showing that there are infinitely many pairwise non-isomorphic filters
of this type.
Research partially supported NSF Grants DMS-96-3465 (Cholak) and DMS-95-00983 (Nies). The authors would like to thank Mike
Stob for his help and interest. 相似文献
10.
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
11.
We prove the existence of a positive and smooth solution for the following semilinear elliptic problem:
% MathType!End!2!1! for anya∈R
N
, 1<p<1+2/N andq=(p+1)/2. This solution decays exponentially as |x|→+∞. Moreover, if |a| is sufficiently small, this positive and rapidly decaying solution is unique.
The existence of a positive, self-similar solution
% MathType!End!2!1! follows for the following convection-diffusion equation with absorption:
% MathType!End!2!1!. It is also a very singular solution. This solution decays as |x|→+∞ for anyt>0 fixed.
Because of the nonvariational nature of the elliptic problem, a fixed point method is used for proving the existence result.
The uniqueness is proved applying the Implicit Function Theorem.
The work of the first author has been partially supported by Grant 1273/00003/88 of the University of the Basque Country.
The work of the second author has been supported by Grant PB 86-0112-C02-00 of the Dirección General de Investigación Científica
y Técnica. 相似文献
12.
Jong Taek Cho 《Israel Journal of Mathematics》1999,109(1):299-318
N. Tanaka ([10]) defined the canonical affine connection on a nondegenerate integrable CR manifold. In the present paper,
we introduce a new class of contact Riemannian manifolds satisfying (C) (
for any unit
-geodesic (
, where
is the generalized Tanaka connection. In particular, when the associated CR structure of a given contact Riemannian manifold
is integrable we have a structure theorem and find examples which are neither Sasakian nor locally symmetric but satisfy the
condition (C).
This work was supported in part by BSRI 98-1425. 相似文献
13.
M. Zippin 《Israel Journal of Mathematics》1966,4(3):199-204
A basis
is constructed inc
0 such that there exists no bounded linear projection ofc
0 onto the subspace spanned by a certain subsequence
of
.
This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the suppervision of Professor
A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful advice. 相似文献
14.
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
15.
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
16.
Michael Kallay 《Israel Journal of Mathematics》1974,17(2):149-161
Let
denote the class of plane convex bodies having a width functionw, wherew′ is absolutely continuous. It is proved that a body in
is determined (up to translation) by the radius of curvature function of its boundary. This result is then used for a characterization
of the extreme (indecomposable) bodies in
and for a density theorem for Reuleaux polygons in
.
The content of this paper is a revised version of a part of the Master of Science thesis written by the author under the supervision
of Professor Micha A. Perles at the Hebrew University of Jerusalem and submitted in October, 1971. 相似文献
17.
Zoé Chatzidakis 《Israel Journal of Mathematics》1986,55(2):173-183
LetK be a hilbertian field,G(K) its absolute Galois group. IfK is countable, then for a.a.
inG(K)
e
,
and there is no intermediate field
with
. Let
∈G(K)
e
. Then for a.a.
in
. 相似文献
18.
A finite state stationary process is defined to be loosely block independent if long blocks are almost independent in the
sense. We show that loose block independence is preserved under Kakutani equivalence and
limits. We show directly that any loosely block independent process is the
limit of Bernoulli processes and is a factor of a process which is Kakutani equivalent to a Bernoulli shift. The existing
equivalence theory then yields that the loosely block independent processes are exactly the loosely Bernoulli (or finitely
fixed) processes. 相似文献
19.
Yehoram Gordon 《Israel Journal of Mathematics》1981,39(1-2):141-144
LetX andY be Banach spaces. TFAE (1)X andY do not contain subspaces uniformly isomorphic to
(2) The local unconditional structure constant of the space of bounded operatorsL (X*k,Y
k) tends to infinity for every increasing sequence
and
of finite-dimensional subspaces ofX andY respectively. 相似文献
20.
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