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The purpose of this paper is to obtain some inequalities for the dimension of the Schur multiplier of a pair of finite dimensional Lie algebras and their factor Lie algebras. Moreover, we present some inequalities for the Schur multiplier of a pair of finite dimensional nilpotent Lie algebras. 相似文献
3.
Mats Erik Andersson 《Proceedings of the American Mathematical Society》2005,133(5):1469-1473
It is shown that a Schur multiplier is compact if and only if it is the Schur product of two multipliers, one of which is a Hankel-Schur multiplier generated by an integrable function. This is illuminated by factoring exotic, singular measures and is brought into relation with Paley set-based multipliers.
4.
首先得到了半正定 Hermitian矩阵的方幂的广义 Schur补的 L owner偏序的一些结果 ,然后改进了半正定 Hermitian矩阵的 Schur补的交错不等式 . 相似文献
5.
In this article, some inequalities of the dimension of Schur multiplier of pairs of Lie algebras will be obtained and new upper bound will be compared with the existing ones in the literature. Furthermore, by using homological methods, we will derive some properties of the higher Schur multiplier of a pair of Lie algebras and give some isomorphisms that generalize some known results of Stallings in group theory setting. 相似文献
6.
Pradeep K. Rai 《代数通讯》2013,41(10):3982-3986
We give a bound on the dimension of the Schur multiplier of a finite dimensional nilpotent Lie algebra which sharpens the earlier known bounds. 相似文献
7.
Pradeep K. Rai 《Archiv der Mathematik》2018,111(2):129-133
We complete the classification of finite p-groups having Schur multiplier of maximum order. 相似文献
8.
G. F. Bachurin 《Mathematical Notes》1969,5(5):325-327
The notion of the Schur multiplier is carried over to torsion-free nilpotent groups of finite rank, and the relation between the rank of a torsion-free nilpotent group and the rank of its multiplier is determined, [3].Translated from Matematicheskie Zametki, Vol. 5, No. 5, pp. 541–544, May, 1969. 相似文献
9.
《Indagationes Mathematicae》2017,28(4):892-912
We study the behavior of some classes of Hilbert space contractions with respect to Harnack and Shmul’yan pre-orders and the corresponding equivalence relations. We give some conditions under which the Harnack equivalence of two given contractions is equivalent to their Shmul’yan equivalence and to the existence of an arc joining the two contractions in the class of operator-valued contractive analytic functions on the unit disc. We apply some of these results to quasi-isometries and quasi-normal contractions, as well as to partial isometries for which we show that their Harnack and Shmul’yan parts coincide. We also discuss an extension, recently considered by S. ter Horst (2014), of the Shmul’yan pre-order from contractions to the operator-valued Schur class of functions. In particular, the Shmul’yan–ter Horst part of a given partial isometry, viewed as a constant Schur class function, is explicitly determined. 相似文献
10.
We study the problem of characterizing Hankel–Schur multipliers and Toeplitz–Schur multipliers of Schatten–von Neumann class
for . We obtain various sharp necessary conditions and sufficient conditions for a Hankel matrix to be a Schur multiplier of . We also give a characterization of the Hankel–Schur multipliers of whos e symbols have lacunary power series. Then the results on Hankel–Schur multipliers are used to obtain a characterization
of the Toeplitz–Schur multipliers of . Finally, we return to Hankel–Schur multipliers and obtain new results in the case when the symbol of the Hankel matrix is
a complex measure on the unit circle.
Received: 16 February 2001 / revised version: 2 December 2001 / Published online: 27 June 2002
The first author is partially supported by Grant 99-01-00103 of Russian Foundation of Fundamental Studies and by Grant 326.53
of Integration. The second author is partially supported by NSF grant DMS 9970561. 相似文献
11.
Ali-Reza Jamali 《Journal of Applied Mathematics and Computing》2004,16(1-2):303-306
There are 49 non-metacyclicp-groups of order less than 1000 with trivial Schur multiplier. In this papar we give a list of deficiency zero presentations for these groups. 相似文献
12.
The Bogomolov multiplier of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. This invariant of G plays an important role in birational geometry of quotient spaces V/G. We show that in many cases the vanishing of the Bogomolov multiplier is guaranteed by the rigidity of G in the sense that it has no outer class-preserving automorphisms. 相似文献
13.
Jihuan He 《Communications in Nonlinear Science & Numerical Simulation》1997,2(4):230-235
In this paper, a novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small perturbations. In this method, a correction functional is constructed by a general Lagrange multiplier, which can be identified via variational theory. An analytical solution can be obtained from its trial-function with possible unknown constants, which can be identified by imposing the boundary conditions, by successively iteration. 相似文献
14.
Graham Ellis 《Applied Categorical Structures》1998,6(3):355-371
In this article we develop the theory of a Schur multiplier for pairs of groups. The idea of such a multiplier is implicit in the work of J.-L. Loday (1978) and others on algebraicK -theory, and in the work of Eckmann et al. (1972) and others on group homology. In contrast to their work, we focus on the general group-theoretic properties of the multiplier. These properties are systematically derived from: 1) the functoriality of the multiplier; 2) an exact homology sequence; 3) and a transfer homomorphism. 相似文献
15.
É. M. Zhmud' 《Ukrainian Mathematical Journal》1995,47(4):634-639
This paper is a sequel of [1]. On the basis of the results obtained therein, we establish inequalities that strengthen the known Green inequality for the order of the Schur multiplier of ap-group.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 546–550, April, 1995. 相似文献
16.
Using computational methods, we first show that there are exactly eighteen 3-generator 2-groups of order 210 with trivial Schur multiplier all having deficiency zero. We next generalize one of the groups obtained to exhibit two infinite classes of 3-generator, 3-relation finite 2-groups of high nilpotency class providing an affirmative answer to a problem posed by Havas et al. 相似文献
17.
Given a collection of test functions, one defines the associated Schur–Agler class as the intersection of the contractive multipliers over the collection of all positive kernels for which each test function is a contractive multiplier. We indicate extensions of this framework to the case where the test functions, kernel functions, and Schur–Agler-class functions are allowed to be matrix- or operator-valued. We illustrate the general theory with two examples: (1) the matrix-valued Schur class over a finitely-connected planar domain and (2) the matrix-valued version of the constrained Hardy algebra (bounded analytic functions on the unit disk with derivative at the origin constrained to have zero value). Emphasis is on examples where the matrix-valued version is not obtained as a simple tensoring with ${{\mathbb C}^{N}}$ of the scalar-valued version. 相似文献
18.
正定矩阵的Khatri-Rao乘积的块Schur补的逆的一些偏序 总被引:8,自引:1,他引:7
给出了分块矩阵的块Schur补的定义,得到一些正定矩阵的Khatri-Rao乘积的块Schur补的逆的偏序,推广了正定矩阵的Hadamare乘积的相应结果。 相似文献
19.
Peyman Niroomand 《Central European Journal of Mathematics》2011,9(1):57-64
Let L be an n-dimensional non-abelian nilpotent Lie algebra and $
s(L) = \frac{1}
{2}(n - 1)(n - 2) + 1 - \dim M(L)
$
s(L) = \frac{1}
{2}(n - 1)(n - 2) + 1 - \dim M(L)
where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has
been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2. 相似文献
20.
Olga Holtz Volker Mehrmann Hans Schneider 《Linear algebra and its applications》2013,438(5):2574-2590
We examine when a matrix whose elements are differentiable functions in one variable commutes with its derivative. This problem was discussed in a letter from Schur to Wielandt written in 1934, which we found in Wielandt’s Nachlass. We present this letter and its translation into English. The topic was rediscovered later and partial results were proved. However, there are many subtle observations in Schur’s letter which were not obtained in later years. Using an algebraic setting, we put these into perspective and extend them in several directions. We present in detail the relationship between several conditions mentioned in Schur’s letter and we focus in particular on the characterization of matrices called Type 1 by Schur. We also present several examples that demonstrate Schur’s observations. 相似文献