共查询到20条相似文献,搜索用时 187 毫秒
1.
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!. |
2.
M. Rovinsky 《Selecta Mathematica, New Series》2009,15(2):343-376
Let G be the automorphism group of an extension of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we
The study of open subgroups is motivated by the study of (the stabilizers of) smooth representations undertaken in [R1, R3].
The functor Γ is an analogue of the global sections functor on the category of sheaves on a smooth proper algebraic variety.
Another result is that ‘interesting’ semilinear representations are ‘globally generated’.
相似文献
• | construct some maximal closed non-open subgroups Gv, and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G; |
• | describe, in the case of countable transcendence degree, the automorphism subgroups over the intermediate subfields (a question of Krull, [K2, §4, question 3b)]); |
• | construct, in the case n = ∞, a fully faithful subfunctor ( − )v of the forgetful functor from the category of smooth representations of G to the category of smooth representations of Gv; |
• | construct, using the functors ( − )v, a subfunctor Γ of the identity functor on , coincident (via the forgetful functor) with the functor Γ on the category of admissible semilinear representations of G constructed in [R3] in the case n = ∞ and . |
3.
John W. Snow 《Algebra Universalis》2005,54(1):65-71
A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Ln is the congruence lattice of an algebra on An for all positive integers n. Let A and B be finite algebras. We prove
Received November 11, 2004; accepted in final form November 23, 2004. 相似文献
• | If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A × B. |
• | If ConA is distributive and ConB is power-hereditary, then (ConA) × (ConB) is powerhereditary. |
• | If ConA ≅ N5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice. |
• | Every congruence lattice representation of N5 is power-hereditary. |
4.
Marie-Claude Arnaud 《Annales Henri Poincare》2008,9(5):881-926
In this article, we prove different results concerning the regularity of the C
0-Lagrangian invariant graphs of the Tonelli flows. For example :
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
• | in dimension 2 and in the autonomous generic case, we prove that such a graph is in fact C 1 on some set with (Lebesgue) full measure; |
• | under certain dynamical additional hypothesis, we prove that these graphs are C 1. |
Résumé. Dans cet article, on démontre différents résultats concernant la régularité des graphes C 0-lagrangiens invariants par des flots de Tonelli. Par exemple :
• en dimension 2, dans le cas autonome et générique, on montre que ces graphes sont de classe C 1 sur un ensemble de mesure (de Lebesque) pleine; • sous certaines hypothèses concernant la dynamique restreinte, on montre que ces graphes sont de classe C 1.
Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
5.
Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian
symmetric spaces which are not semisimple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal
modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric
space M to a triple consisting of:
That leads to a classification scheme of indecomposable nonsimple pseudo-Riemannian symmetric spaces. In addition, we obtain
a full classification of symmetric spaces of index 2 (thereby completing and correcting in part earlier classification results
due to Cahen and Parker and to Neukirchner). 相似文献
(i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M); | |
(ii) a semisimple orthogonal module of the Lie algebra with involution; and | |
(iii) a quadratic cohomology class of this module. |
6.
Nikita A. Karpenko 《manuscripta mathematica》1995,88(1):109-117
We compute degrees of algebraic cycles on certain Severi-Brauer varieties and apply it to show that:
This article was processed by the author using the LATEX style filecljour 1 from Springer-Verlag 相似文献
– | - a generic division algebra of indexp α and exponentp is not decomposable (in a tensor product of two algebras) for any primep and any α except the case whenp=2 and 2 | α; |
– | - the 2-codimensional Chow group CH2 of the Severi-Brauer variety corresponding to the generic division algebra of index 8 and exponent 2 has a non-trivial torsion. |
7.
8.
Let X be a Banach space and let (ξj)j ≧ 1 be an i.i.d. sequence of symmetric random variables with finite moments of all orders. We prove that the following assertions
are equivalent:
Received: 10 January 2005; revised: 5 April 2005 相似文献
1. |
There exists a constant K such that
|
|
2. | X is isomorphic to a Hilbert space. |
9.
This article gives relations between two types of phase space distributions associated to eigenfunctions
of the Laplacian on a compact hyperbolic surface X
Γ:
We prove that these distributions (when suitably normalized) are asymptotically equal as
. We also give exact relations between them. This correspondence gives a new relation between classical and quantum dynamics
on a hyperbolic surface, and consequently a formulation of quantum ergodicity in terms of classical ergodic theory.
Research partially supported by NSF grant #DMS-0302518 and NSF Focussed Research Grant # FRG 0354386.
Submitted: April 20, 2006. Revised: July 10, 2006. Accepted: July 31, 2006. 相似文献
• | Wigner distributions , which arise in quantum chaos. They are invariant under the wave group. |
• | Patterson-Sullivan distributions , which are the residues of the dynamical zeta-functions (where the sum runs over closed geodesics) at the poles s = 1/2 + irj. They are invariant under the geodesic flow. |
10.
We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on
a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic stationary
measures always exist, and when such a measure has full support, we show the following:
An important ingredient in the proofs is a generalization of Gromov’s centralizer theorem beyond the case of invariant measures. 相似文献
1. | Either the manifold admits a smooth equivariant map onto a homogeneous projective variety, defined on an open dense conull invariant set, or the Lie algebra of the Zariski closure of the Gromov representation of the fundamental group contains a Lie subalgebra isomorphic to the Lie algebra of the acting group. As a corollary, a smooth non-trivial homogeneous projective factor does exist whenever the fundamental group of M admits only virtually solvable linear representations, and thus in particular when M is simply connected, regardless of the real rank. |
2. | There exist explicit examples showing that analytic rigid actions of certain simple real rank one groups may indeed fail to have a smooth projective factor. |
3. | It is possible to generalize Gromov’s theorem on the algebraic hull of the representation of the fundamental group of the manifold to the case of rigid non-unimodular structures, again for actions of groups of any real rank. |
11.
Paweł Głowacki 《Arkiv f?r Matematik》2007,45(1):31-48
The purpose of this note is to give an extension of the symbolic calculus of Melin for convolution operators on nilpotent
Lie groups with dilations. Whereas the calculus of Melin is restricted to stratified nilpotent groups, the extension offered
here is valid for general homogeneous groups. Another improvement concerns the L
2-boundedness theorem, where our assumptions on the symbol are relaxed. The zero-class conditions that we require are of the
type
where ρ
j
are “partial homogeneous norms” depending on the variables ξ
k
for k>j in the natural grading of the Lie algebra (and its dual) determined by dilations. Finally, the class of admissible weights
for our calculus is substantially broader. Let us also emphasize the relative simplicity of our argument compared to that
of Melin. 相似文献
12.
Hans Peter Schlickewei Wolfgang M. Schmidt Michel Waldschmidt 《manuscripta mathematica》1999,98(2):225-241
Let be an exponential polynomial over a field of zero characteristic. Assume that for each pair i,j with i≠j, α
i
/α
j
is not a root of unity. Define . We introduce a partition of into subsets (1≤i≤m), which induces a decomposition of f into , so that, for 1≤i≤m, , while for , the number either is transcendental or else is algebraic with not too small a height. Then we show that for all but at most solutions x∈ℤ of f(x)= 0, we have
Received: 7 August 1998 相似文献
13.
We investigate the large time behavior of positive solutions with finite mass for the viscous Hamilton-Jacobi equationu
t
= Δu + |Δu|
p
,t>0,x ∈ ℝ
N
, wherep≥1 andu(0,.)=u
0≥0,u
0≢0,u
0∈L
1. DenotingI
∞=lim
t→∞‖u(t)‖1≤∞, we show that the asymptotic behavior of the mass can be classified along three cases as follows:
We also consider a similar question for the equationu
t=Δu+u
p
. 相似文献
– | • ifp≤(N+2)/(N+1), thenI ∞=∞ for allu 0; |
– | • if (N+2)/(N+1)<p<2, then bothI ∞=∞ andI ∞<∞ occur; |
– | • ifp≥2, thenI ∞<∞ for allu 0. |
14.
Joseph Corneli Neil Hoffman Paul Holt George Lee Nicholas Leger Stephen Moseley Eric Schoenfeld 《Journal of Geometric Analysis》2007,17(2):189-212
We prove the double bubble conjecture in the three-sphereS
3 and hyperbolic three-spaceH
3 in the cases where we can apply Hutchings theory:
A balancing argument and asymptotic analysis reduce the problem inS
3 andH
3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces. 相似文献
– | • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3. |
– | • inH 3, when the smaller volume is at least 85% that of the larger. |
15.
Kenley Jung 《Mathematische Annalen》2007,338(1):241-248
Suppose M is a tracial von Neumann algebra embeddable into (the ultraproduct of the hyperfinite II1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k ,γ). We say that X is tubular if for any ε > 0 there exist and γ > 0 such that if then there exists a k × k unitary u satisfying for each 1 ≤ i ≤ n. We show that the following conditions are equivalent:
Research supported in part by the NSF.
Dedicated to Ed Effros on the occasion of his 70th birthday. 相似文献
• | M is amenable (i.e., injective). |
• | X is tubular. |
• | Any two embeddings of M into are conjugate by a unitary . |
16.
Two partial ordersP andQ on a setX arecomplementary (written asPQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integern we form a graph Pos
n
consisting of all nonempty partial orders on {1, ,n} with edges denoting complementation. We investigate here properties of the graphs Pos
n
. In particular, we show:
| The diameter of Pos n is 5 for alln>2 (and hence Pos n is connected for alln); | |||||||||||||||||||||||
| With probability 1, the distance between two members of Pos n is 2; | |||||||||||||||||||||||
| The graphs Pos n are universal (i.e. every graph occurs as an induced subgraph of some Pos n ); | |||||||||||||||||||||||
|
The maximal size (n) of an independent set of Pos
n
satisfies the asymptotic formula
|