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1.
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
2.
Let D ⊂ ℜ2 be simply connected. A subset K ⊂ D is relatively convex if a, b ∈ K, [a, b] ⊂ D implies [a, b] ⊂ K. We establish the following version of Helly’s Topological Theorem: If
is a family of (at least 3) compact, polygonally connected and relatively convex subsets of D, then
, provided each three members of
meet.
We also prove other results related to the combinatorial metric ρK(a, b) (= smallest number of edges of a polygonal path from a to b in K). 相似文献
3.
Motivated by the categorical notion of localizations applied to the quasi-category of abelian groups, we call a homomorphism
α: A → B a quasi-localization of abelian groups if for each ϕ ∈ Hom(A,B) there is an n ∈ ℕ and a unique ψ ∈ End(B) such that nϕ = ψ ∘ α. In this case we call B a quasi-localization of A. In this paper we investigate quasi-localizations of the integers ℤ. While it is well-known that localizations of ℤ are just
the E-rings, quasi-localizations of ℤ are much more abundant; an injection α: ℤ → M with M torsion-free, is a quasi-localization if and only if, for R = End(M), one has
. We call R the ring of the quasi-localization M. Some old results due to Zassenhaus and Butler show that all rings with free additive groups of finite rank are indeed rings
of quasi-localizations of ℤ. We will extend this result and show that there are also rings of infinite rank with this property.
While there are many realization results of rings R as endomorphism rings of torsion-free abelian groups M in the literature, the group M is usually not contained in the divisible hull of R
+, as is required here. We will use a particular case of a category of left R-modules M with a distinguished family
of submodules and thus
. We will restrict our discussion to the case M = R such that
, and in this case we call the family
of left ideals E-forcing, not to be confused with the notion of forcing in set theory. We will provide many examples of quasi-localizations
M of ℤ, among them those of infinite rank as well as matrix rings for various rings of finite rank. 相似文献
4.
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
5.
S. Mattarei 《Israel Journal of Mathematics》2009,171(1):1-14
A study of the set of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of
characteristic p > 0 was initiated by Shalev and continued by the present author. The main goal of this paper is to produce more elements
of . Our main result shows that any divisor n of q − 1, where q is a power of p, such that n ≥ (p − 1)1/p
(q − 1)1−1/(2p), necessarily belongs to . This extends its special case for p = 2 which was proved in a previous paper by a different method. 相似文献
6.
Matej Brear 《Israel Journal of Mathematics》2007,162(1):317-334
7.
Let S be a compact, connected, orientable surface of positive genus. Let
be the Hatcher-Thurston complex of S. We prove that Aut
is isomorphic to the extended mapping class group of S modulo its center.
The first author is supported by a Rackham Faculty Fellowship, Horace H. Rackham School of Graduate Studies, University of
Michigan.
The second author is supported in part by the Turkish Academy of Sciences under the Young Scientists Award Program (MK/TüBA-GEBİP
2003-10). 相似文献
8.
If H is a Hopf algebra with bijective antipode and α, β ∈ Aut
Hopf
(H), we introduce a category
, generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category
having all the categories
as components, which, if H is finite dimensional, coincides with the representations of a certain quasitriangular T-coalgebra DT(H) that we construct. We also prove that if (α, β) admits a so-called pair in involution, then
is isomorphic to the category of usual Yetter-Drinfeld modules
.
Research partially supported by the programme CERES of the Romanian Ministry of Education and Research, contract no. 4-147/2004. 相似文献
9.
Let
be finite relational structure of finite type, and let CSP
denote the following decision problem: if
is a given structure of the same type as
, is there a homomorphism from
to
? To each relational structure
is associated naturally an algebra
whose structure determines the complexity of the associated decision problem. We investigate those finite algebras arising
from CSP’s of so-called bounded width, i.e., for which local consistency algorithms effectively decide the problem. We show that if a CSP has bounded width then
the variety generated by the associated algebra omits the Hobby-McKenzie types 1 and 2. This provides a method to prove that
certain CSP’s do not have bounded width. We give several applications, answering a question of Nešetřil and Zhu [26], by showing
that various graph homomorphism problems do not have bounded width. Feder and Vardi [17] have shown that every CSP is polynomial-time
equivalent to the retraction problem for a poset we call the Feder − Vardi poset of the structure. We show that, in the case where the structure has a single relation, if the retraction problem for the
Feder-Vardi poset has bounded width then the CSP for the structure also has bounded width. This is used to exhibit a finite
order-primal algebra whose variety admits type 2 but omits type 1 (provided P ≠ NP).
Presented by M. Valeriote.
Received January 8, 2005; accepted in final form April 3, 2006.
The first author’s research is supported by a grant from NSERC and the Centre de Recherches Mathématiques. The second author’s
research is supported by OTKA no. 034175 and 48809 and T 037877. Part of this research was conducted while the second author
was visiting Concordia University in Montréal and also when the first author was visiting the Bolyai Institute in Szeged.
The support of NSERC, OTKA and the Bolyai Institute is gratefully acknowledged. 相似文献
10.
We consider Dirichlet spaces (
) in L
2 and more general energy forms
in L
p
,
. For the latter we introduce the notions of an extended ’Dirichlet’ space and a transient form. Under the assumption that
, resp.
, are compactly embedded in L
2, resp. L
p
, we prove a Poincaré inequality for transient (Dirichlet) forms. If both
and its adjoint
are sub-Markovian semigroups, we show that the transience of T
t
is independent of
) and that it is implied by the transience of the energy form
of
and the form
belonging to
. 相似文献
11.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
12.
For an l-graph
, the Turán number
is the maximum number of edges in an n-vertex l-graph
containing no copy of
. The limit
is known to exist [8]. The Ramsey–Turán density
is defined similarly to
except that we restrict to only those
with independence number o(n). A result of Erdős and Sós [3] states that
as long as for every edge E of
there is another edge E′of
for which |E∩E′|≥2. Therefore a natural question is whether there exists
for which
.
Another variant
proposed in [3] requires the stronger condition that every set of vertices of
of size at least εn (0<ε<1) has density bounded below by some threshold. By definition,
for every
. However, even
is not known for very many l-graphs
when l>2.
We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we
construct, for each l≥3, infinitely many l-graphs
for which
.
We also prove that the 3-graph
with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies
. The existence of a hypergraph
satisfying
was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based
on different ideas and is simpler than these earlier proofs.
* Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P.
Sloan Research Fellowship.
† Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529. 相似文献
13.
We extend the results of Shalev [Sh] on the orders of nonsingular derivations of finite-dimensional non-nilpotent modular
Lie algebras.
The author is grateful to Ministero dell’Università e della Ricerca Scientifica, Italy, for financial support to the project
“Graded Lie algebras and pro-p-groups of finite width”. 相似文献
14.
S. Norvidas 《Lithuanian Mathematical Journal》2008,48(1):92-99
Let
be a complex unital Banach algebra. An element a ∈
is said to be Hermitian if ‖exp(ita)‖ = 1 for all t ∈ ℝ. In the case of the algebra of bounded linear operators in a Hilbert space, this Hermitian property agrees with the ordinary
self-adjointness. If a ∈
is Hermitian, then ‖a‖ = |a|, where |a| denotes the spectral radius of a. A function F: ℝ → ℂ is called a universal symbol if ‖F(a)‖ = | F(a)| for every
and all Hermitian a ∈
. We characterize universal symbols in terms of positive-definite functions. 相似文献
15.
Amol Sasane 《Integral Equations and Operator Theory》2007,59(2):245-256
Let E, E* be separable Hilbert spaces. If S is an open subset of
, then
denotes the space of all functions
that are holomorphic in
, and bounded and continuous on
. In this article we prove the following results:
相似文献
1. | A theorem concerning the approximation of by a function F that is holomorphic in a neighbourhood of and such that the error F − f is uniformly bounded in the disk . |
2. | The corona theorem for when dim(E) < ∞: If there exists a δ > 0 such that for all , , then there exists a such that for all , g(z)f(z) = I. |
3. | The problem of complementing to an isomorphism for when {dim(E) < ∞ (Tolokonnikov’s lemma): has a left inverse iff it is a ‘part’ of an invertible element F in . |
16.
Rolf Farnsteiner 《Inventiones Mathematicae》2006,166(1):27-94
Given an algebraically closed field k of characteristic p≥3, we classify the finite algebraic k-groups whose algebras of measures afford a principal block of tame representation type. The structure of such a group
is largely determined by a linearly reductive subgroup scheme
of SL(2), with the McKay quiver of
relative to its standard module being the Gabriel quiver of the principal block
. The graphs underlying these quivers are extended Dynkin diagrams of type
or
, and the tame blocks are Morita equivalent to generalizations of the trivial extensions of the radical square zero tame hereditary
algebras of the corresponding type. 相似文献
17.
For two complex Banach spaces X and Y,
(B
X; Y) will denote the space of bounded and continuous functions from B
X
to Y that are holomorphic on the open unit ball. The numerical radius of an element h in
(B
X; X) is the supremum of the set
. We prove that every complex Banach space X with the Radon-Nikodym property satisfies that the subset of numerical radius attaining functions in
(B
X; X) is dense in
(B
X; X). We also show the denseness of the numerical radius attaining elements of
in the whole space, where
is the subset of functions in
which are uniformly continuous on the unit ball. For C(K) we prove a denseness result for the subset of the functions in
(B
C(K); C(K)) which are weakly uniformly continuous on the closed unit ball. For a certain sequence space X, there is a 2-homogenous polynomial P from X to X such that for every R > e, P cannot be approximated by bounded and numerical radius attaining holomorphic functions defined on RB
X
. If Y satisfies some isometric conditions and X is such that the subset of norm attaining functions of
(B
X; ℂ) is dense in
(B
X; ℂ), then the subset of norm attaining functions in
(B
X; Y) is dense in the whole space.
The first author was supported in part by D.G.E.S. Project BFM2003-01681.
The second author’s work was performed during a visit to the Departamento de Análisis Matem’atico of Universidad de Granada,
with a grant supported by the Korea Research Foundation under grant (KRF-2002-070-C00006). 相似文献
18.
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
19.
If
is an initially hereditary family of finite subsets of positive integers (i.e., if
and G is initial segment of F then
) and M an infinite subset of positive integers then we define an ordinal index
. We prove that if
is a family of finite subsets of positive integers such that for every
the characteristic function χF is isolated point of the subspace
of { 0,1 }N with the product topology then
for every
infinite, where
is the set of all initial segments of the members of
and ω1 is the first uncountable ordinal. As a consequence of this result we prove that
is Ramsey, i.e., if
is a partition of
then there exists an infinite subset M of positive integers such that
where [M]< ω is the family of all finite subsets of M. 相似文献
20.
Michael Capalbo 《Combinatorica》2005,25(4):379-391
Here we solve an open problem considered by various researchers by presenting the first explicit constructions of an infinite
family
of bounded-degree ‘unique-neighbor’ concentrators Γ; i.e., there are strictly positive constants α and ε, such that all Γ = (X,Y,E(Γ)) ∈
satisfy the following properties. The output-set Y has cardinality
times that of the input-set X, and for each subset S of X with no more than α|X| vertices, there are at least ε|S| vertices in Y that are adjacent in Γ to exactly one vertex in S. Also, the construction of
is simple to specify, and each
has fewer than
edges. We then modify
to obtain explicit unique-neighbor concentrators of maximum degree 3.
* Supported by NSF grant CCR98210-58 and ARO grant DAAH04-96-1-0013. 相似文献