共查询到20条相似文献,搜索用时 31 毫秒
1.
V. N. Zhelyabin 《代数通讯》2013,41(2):561-576
Let (V, Δ) be a Jordan copair over a field Φ and let V? be its dual pair. Then there exists a Lie coalgebra (L c (V), Δ L ) whose dual algebra (L c (V))? is the Kantor–Koecher–Tits construction for the pair V?. If Φ is a field of characteristic other than 2 or 3 then the Lie coalgebra (L c (J), Δ L ) is locally finite-dimensional. As a corollary we derive that Jordan copairs over fields of characteristic other than 2 or 3 are locally finite-dimensional. 相似文献
2.
V. N. Zhelyabin 《Siberian Mathematical Journal》2005,46(6):1050-1061
W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove that a simple infinite-dimensional Jordan superalgebra of vector type possesses a nonzero dual coalgebra. Thereby, we demonstrate that the hypothesis formulated by W. Michaelis for Lie coalgebras fails in the case of Jordan supercoalgebras. 相似文献
3.
Wayne Neidhardt 《Algebras and Representation Theory》1998,1(2):161-168
We prove the following result for a not necessarily symmetrizable Kac–Moody algebra: Let x,y W with x y, and let P+. If n=l(x)-l(y), then Ext C()
n
(M(x·),L(y·))=1. 相似文献
4.
V. N. Zhelyabin 《Algebra and Logic》1996,35(2):96-104
The relationship between Jordan and Lie coalgebras is established. We prove that from any Jordan coalgebra 〈L(A), Δ〉, it is
possible to construct a Lie coalgebra 〈L(A), ΔL〉. Moreover, any dual algebra of the coalgebra 〈L(A), ΔL〉 corresponds to a Lie algebra that can be determined from the dual algebra for (A, Δ), following the Kantor-Koecher-Tits
process. The structure of subcoalgebras and coideals of the coalgebra 〈L(A), ΔL〉 is characterized.
Supported by ISF grant No. RB 6000.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 173–189, March–April, 1996. 相似文献
5.
Let * be the equilateral triangulation of the plane and let 1
* be the equilateral triangle formed by four triangles of *. We study the space of piecewise polynomial functions in C
k
(R
2) with support 1
*, having a sufficiently high degree n and which are invariant with respect to the group of symmetries of 1
*. Such splines are called 1
*-splines. We first compute the dimension of this space in function of n and k. Then, for any fixed k0, we prove the existence of 1
*-splines of class C
k
and minimal degree, but these splines are not unique. Finally, we describe an algorithm computing the Bernstein–Bézier coefficients of these splines. 相似文献
6.
Let H be a Hopf k-algebra. We study the global homological dimension of the underlying coalgebra structure of H. We show that gl.dim(H) is equal to the injective dimension of the trivial right H-comodule k. We also prove that if D = C H is a crossed coproduct with invertible , then gl.dim(D) gl.dim(C) + gl.dim(H). Some applications of this result are obtained. Moreover, if C is a cocommutative coalgebra such that C
* is noetherian, then the global dimension of the coalgebra C coincides with the global dimension of the algebra C
*. 相似文献
7.
Nikolov N. M. Stanev Ya. S. Todorov I. T. 《Theoretical and Mathematical Physics》2002,132(2):1148-1162
We use the recently established rationality of correlation functions in a globally conformally invariant quantum field theory satisfying Wightman axioms to construct a family of solvable models in the four-dimensional Minkowski space–time. We consider the model of a neutral two-dimension scalar field in detail. It depends on a positive real parameter c, an analogue of the Virasoro central charge; for all (finite) c, it admits an infinite number of conserved symmetric tensor currents. The operator product algebra of coincides with a simpler one generated by a bilocal scalar field V(x
1,x
2) of dimension 1+1. The modes of V together with the unit operator span an infinite-dimensional Lie algebra
V
, whose vacuum (i.e., zero-energy lowest-weight) representations depend only on the central charge c. The Wightman positivity (i.e., unitarity of the representations of
V
) is proved equivalent to c. 相似文献
8.
Let e(x, y, ) be the spectral function and the unit spectral projection operator, with respect to the Laplace–Beltrami operator on a closed Riemannian manifold M. We generalize the one-term asymptotic expansion of e(x, x, ) by Hörmander (Acta Math.
88 (1968), 341–370) to that of
x
y
e(x,y,)|
x=y
for any multiindices , in a sufficiently small geodesic normal coordinate chart of M. Moreover, we extend the sharp (L
2,L
p) (2 p) estimates of by Sogge (J. Funct. Anal.
77 (1988), 123–134; London Math. Soc. Lecture Note Ser. 137, Cambridge University Press, Cambridge, 1989; Vol. 1, pp. 416–422) to the sharp (L
2, Sobolev L
p) estimates of . 相似文献
9.
10.
The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm
must be isomorphic toW(m,n, 1) if the dimension ofG
i satisfies a certain condition.
Project supported by the National Natural Science Foundation of China and the Science of the University Doctoral Program of
CNEC. 相似文献
11.
A Strong Maximum Principle for some quasilinear elliptic equations 总被引:37,自引:0,他引:37
J. L. Vázquez 《Applied Mathematics and Optimization》1984,12(1):191-202
In its simplest form the Strong Maximum Principle says that a nonnegative superharmonic continuous function in a domain
n
,n 1, is in fact positive everywhere. Here we prove that the same conclusion is true for the weak solutions of – u + (u) = f with a nondecreasing function ,(0)=0, andf0 a.e. in if and only if the integral((s)s)
–1/2
ds diverges ats=0+. We extend the result to more general equations, in particular to –
p
u + (u) =f where
p
(u) = div(|Du|
p-2
Du), 1 <p < . Our main result characterizes the nonexistence of a dead core in some reaction-diffusion systems.This work was partly done while the author was visiting the University of Minnesota as a Fulbright Scholar. 相似文献
12.
13.
Indira Chatterji 《Geometriae Dedicata》2003,96(1):161-177
We apply V. Lafforgues techniques to establish property (RD) for cocompact lattices in a finite product of rank one Lie groups with Lie groups whose restricted root system is of type A
2. 相似文献
14.
We prove that any quasiassociative algebra with simple Artinian null part is isomorphic to a unique matrix algebra Mn(), where is a quasiassociative division algebra. 相似文献
15.
Salvatore A. Marano 《Set-Valued Analysis》1996,4(3):287-300
Let be a bounded domain in n (n3) having a smooth boundary, let be an essentially bounded real-valued function defined on × h, and let be a continuous real-valued function defined on a given subset Y of Y h. In this paper, the existence of strong solutions u W
2,p (, h) W
o
1,p
(n/2<p<+) to the implicit elliptic equation (–u)=(x,u), with u=(u1, u2, ..., uh) and u=(u
1, u
2, ..., u
h), is established. The abstract framework where the problem is placed is that of set-valued analysis. 相似文献
16.
Consider a functionL() defined on an interval of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point 0 and a vector
0 H(
0 0) are called eigenvalue and eigenvector ofL() ifL() ifL(0)
0 = 0. Supposing that the functionL() can be represented as an absolutely convergent Fourier integral, the interval is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL() corresponding to the eigenvalues from the interval form an unconditional basis in the subspace spanned by them. 相似文献
17.
Séverine Leidwanger 《Journal of Algebraic Combinatorics》2001,14(2):133-144
The infinite dimensional Lie algebra l
n = A
n–1
(1) can be realized in several ways as an algebra of differential operators. The aim of this note is to show that the intertwining operators between the realizations of l
n corresponding to all partitions of n can be described very simply by using combinatorial constructions. 相似文献
18.
For a complete manifold M with constant negative curvature, weprove that the rough Laplacian
R
defines topological isomorphisms in the scale of Sobolev spaces H
p
s
(M) ofp-forms for all p, 0 < p< n. For the de Rham Laplacian and M=
n
, the Poincaréhyperbolic space, this is shown too for 0 pn,pn/2, p (n± 1)/2. 相似文献
19.
Q. Mushtaq 《Southeast Asian Bulletin of Mathematics》2001,25(2):309-312
In this paper we are interested in triangle groups (j, k, l) where j = 2 and k = 3. The groups (j, k, l) can be considered as factor groups of the modular group PSL(2, Z) which has the presentation x, y : x2 = y3 = 1. Since PSL(2,q) is a factor group of Gk,l,m if -1 is a quadratic residue in the finite field Fq, it is therefore worthwhile to look at (j, k, l) groups as subgroups of PSL(2, q) or PGL(2, q). Specifically, we shall find a condition in form of a polynomial for the existence of groups (2, 3, k) as subgroups of PSL(2, q) or PGL(2, q).Mathematics Subject Classification: Primary 20F05 Secondary 20G40. 相似文献
20.
Let be a triangle in
and let
be the set of its three medians. We construct interpolants to smooth functions using transfinite (or blending) interpolation on
The interpolants are of type f(1)+g(2)+h(3), where (1,2,3) are the barycentric coordinates with respect to the vertices of . Based on an error representation formula, we prove that the interpolant is the unique best L1-approximant by functions of this type subject the function to be approximated is from a certain convexity cone in C3().Received: 17 December 2003 相似文献