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2.
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:
| |
(i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M);
|
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(ii) a semisimple orthogonal module of the Lie algebra with involution; and |
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(iii) a quadratic cohomology class of this module. |
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
3.
Rings over which every nonzero right module has a maximal submodule are called right Bass rings. For a ring A module-finite over its center C, the equivalence of the following conditions is proved: | (1) |
A is a tight Bass ring;
| | (2) |
A is a left Bass ring;
| | (3) |
A/J(A) is a regular ring, andJ(A) is a right and leftt-nilpotent ideal.
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Translated from Matematicheskie Zametki, Vol. 64, No. 1, pp. 136–142, July, 1998.This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00627. 相似文献
4.
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
| – |
• is finitely generated and infinite-dimensional, but has only finitedimensional quotients;
|
| – |
• has a subalgebra of finite codimension, isomorphic toM
2(k);
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• is prime;
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• has quadratic growth, and therefore Gelfand-Kirillov dimension 2;
|
| – |
• is recursively presented;
|
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• satisfies no identity;
|
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• contains a transcendental, invertible element;
|
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• is semiprimitive if
% MathType!End!2!1! has characteristic ≠2;
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• 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!.
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The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
5.
Two partial orders P and Q on a set X are complementary (written as PQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integer n 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|
相似文献
6.
In this article, we prove different results concerning the regularity of the C
0-Lagrangian invariant graphs of the Tonelli flows. For example :
| •
|
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;
|
| •
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under certain dynamical additional hypothesis, we prove that these graphs are C
1.
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Résumé. Dans cet article, on démontre différents résultats concernant la régularité des graphes C
0-lagrangiens invariants par des flots de Tonelli. Par exemple :
| •
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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;
|
| •
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sous certaines hypothèses concernant la dynamique restreinte, on montre que ces graphes sont de classe C
1.
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Submitted: July 23, 2007. Accepted: February 14, 2008. 相似文献
7.
Game trees are an important model of decision-making situations, both in artificial intelligence and decision analysis. The model most frequently investigated in theoretical research consists of a uniform tree of heigh h and a constant branching factor b, where the terminal positions are assigned the values of independent, identically distributed random variables [1, 3–10]. Our paper investigates two generalizations:
| 1. |
Different levels of the tree may have different branching factors.
| | 2. |
The preferences of the two players may no longer be totally opposite.
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相似文献
8.
Let H
1, H
2 be Hilbert spaces and T be a closed linear operator defined on a dense subspace D( T) in H
1 and taking values in H
2. In this article we prove the following results:
| (i) |
Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H
1 = H
2 and T is self-adjoint, then
|
| (ii) |
inf {‖T x‖: x ∈ D(T) ∩ N(T)⊥‖x‖ = 1} = inf {|λ|: 0 ≠ λ ∈ σ(T)}
|
| (iii) |
Every isolated spectral value of T is an eigenvalue of T
|
| (iv) |
Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T) of T
|
| (v) |
σ(T) bounded implies T is bounded.
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We prove all the above results without using the spectral theorem. Also, we give examples to illustrate all the above results. 相似文献
9.
| 1. |
Letm be the greatest integer such that
. ThenPG(3,q) contains complete caps of sizek=(m+1)(q+1)+ω, with ω=0, 1, 2.
|
| 2. |
PG(3,q),q≥5, contains complete caps of size.
|
| 3. |
InPG(3,q) complete caps different from ovaloids have some external planes.
|
相似文献
10.
We present a new pivot-based algorithm which can be used with minor modification for the enumeration of the facets of the
convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary
dimension. The algorithm has the following properties:
| (a) |
Virtually no additional storage is required beyond the input data.
|
| (b) |
The output list produced is free of duplicates.
|
| (c) |
The algorithm is extremely simple, requires no data structures, and handles all degenerate cases.
|
| (d) |
The running time is output sensitive for nondegenerate inputs.
|
| (e) |
The algorithm is easy to parallelize efficiently.
|
For example, the algorithm finds the v vertices of a polyhedron in R
d defined by a nondegenerate system of n inequalities (or, dually, the v facets of the convex hull of n points in R
d, where each facet contains exactly d given points) in time O( ndv) and O( nd) space. The v vertices in a simple arrangement of n hyperplanes in R
d can be found in O( n
2
dv) time and O( nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming. 相似文献
11.
We compute degrees of algebraic cycles on certain Severi-Brauer varieties and apply it to show that:
| – |
- 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;
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| – |
- 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.
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This article was processed by the author using the LATEX style file cljour 1 from Springer-Verlag 相似文献
12.
I have exhibited several types of monotiles with matching rules that force the construction of a hexagonal parquet. The isohedral
number of the resulting tiling can be made as large as desired by increasing the aspect ratio of the monotile. Aside from
illustrating some elegant peculiarities of the hexagonal parquet tiling, the constructions demonstrate three points.
| 1. |
Monotiles with arbitrarily large isohedral number do exist; |
| 2. |
The additional topological possibilities afforded in 3D allow construction of a simply connected monotile with a rule enforced
by shape only, which is impossible for the hexagonal parquet in 2D;
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| 3. |
The precise statement of the tiling problem matters— whether color matching rules are allowed; whether multiply connected
shapes are allowed; whether spacefilling is required as opposed to just maximum density. So what about the quest for thek = ∞ monotile? Schmitt.
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相似文献
13.
In this paper, we study non-singular solutions to Ricci flow on a closed manifold of dimension at least 4. Amongst other things
we prove that, if M is a closed 4-manifold on which the normalized Ricci flow exists for all time t > 0 with uniformly bounded sectional curvature, then the Euler characteristic . Moreover, the 4-manifold satisfies one of the followings
| (i) |
M is a shrinking Ricci soliton;
|
| (ii) |
M admits a positive rank F-structure;
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| (iii) |
the Hitchin–Thorpe type inequality holds |
where (resp. ) is the Euler characteristic (resp. signature) of M.
The first author was supported by a NSF Grant of China and the Capital Normal University. 相似文献
14.
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
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If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A × B.
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If ConA is distributive and ConB is power-hereditary, then (ConA) × (ConB) is powerhereditary.
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If ConA ≅ N5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice.
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| •
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Every congruence lattice representation of N5 is power-hereditary.
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Received November 11, 2004; accepted in final form November 23, 2004. 相似文献
15.
The major sequences of length n are defined as the words with n letters taken from the integers 1, 2, , n and containing at least
| 1. |
letter equal ton
| | 2. |
letters equal or more thann – 1,n – 1 letters equal or more than 2.
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相似文献
16.
We consider games in coalition function form on a, generally infinite, algebra of coalitions. For finite algebras the additive part mapping v E( v ¦) is the usual. The concern here is the analogue for infinite algebras. The useful construction is the finitely additive stochastic process of additive parts of the game on the filtration
f
of finite subalgebras of.It is shown that
is an isomorphism between: | a) |
Additive games and martingales
| | b) |
Superadditive games and supermartingales
| | c) |
Shapley's games of bounded deviationBD() in his (1953) dissertation and bounded F-processes of Armstrong (1983)
| | d) |
Gilboa's spaceBS() (1989) and bounded processes of Armstrong (1983)
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相似文献
17.
A nearlattice S is a meet semilattice together with the property that any two elements possessing a common upper bound have a supremum. Here the authors have introduced the notion of sectionally semicomplemented distributive nearlattices and given several characterizations of them. The skeleton SCon( S) of Con( S), the congruence lattice, consists of all those nearlattice congruences which are the pseudocomplements of members of Con( S). The relationship between skeletal congruences and kernel of skeletal congruences leads to numerous characterizations of sectionally semicomplemented distributive nearlattices and semiboolean algebras. For example we prove, for a distributive nearlattice S with 0, the following conditions are equivalent:
| (i) | S is sectionally semicomplemented | | (ii) | The map Θ Θ ̸ker Θ of SCon(S) onto KSCon(S) is one-to-one. | | (iii) | The map Θ Θ ̸ker Θ of SCon(S) onto KSCon(S) preserves finite joins. | | (iv) | The map Θ Θ ker ̸Θ is a lattice isomorphism of SCon(S) onto KSCon(S), whose inverse is the map J ̸ Θ(J)**. |
AMS Subject Classifications (1991): 06A12, 06A99, 06B10. 相似文献
18.
Let F( X, Y) be a two dimensional polynomial map over C. We show how to use the notion of induced resultants in order to give short and elementary proofs to the following three
theorems:
| 1. |
If the Jacobian of F is a non-zero constant, then the image of F contains all of C2 except for a finite set.
|
| 2. |
If F is invertible, then the inverse map is determined by the free terms of the induced resultants.
|
| 3. |
If F is invertible, then the degree of F equals the degree of its inverse.
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相似文献
19.
We have generalized the theory of Shannon's games in [10]. In this paper, we treat a game on a graph with an action of elementary abelian group but our decision of the winner is more general. Our theory can be applied for non-negative integers n and r, to the two games on a graph with n + 1 distinguished terminals whose rules are as follows: | (1) |
the players Short and Cut play alternately to choose an edge,
| | (2) |
the former contracts it and the later deletes it
| | (3) |
the former
if and only if he connects the terminals into at mostn – r + 1 ones.
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Dedicated to Professor Sin Hitotumatu for his 60'th birthday 相似文献
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