共查询到20条相似文献,搜索用时 31 毫秒
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Inmaculada Lizasoain 《Algebras and Representation Theory》2011,14(4):639-663
In this paper we establish a decomposition theorem for an ordinary representation of a finite group G in any category C{\mathcal C} which expresses a suitable irreducible representation of G as the tensor product of two projective ones. The celebrated theorem due to Clifford for a linear representation turns out
to be a particular case of it. For that purpose, a definition of projective extension of an ordinary representation of a normal
subgroup of G is introduced, as well as a tensor product between two of them. 相似文献
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By the decomposition theorem dim X ≦ n if and only if X admits a decomposition into n+1 zero-dimensional subspaces Z i for i = 0,... n. If f: X → X is a homeomorphism, then under some dimensional restrictions on the set of periodic points, the Z i can be chosen to be images of Z 0 under iterates of f. 相似文献
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In this paper, we generalize the splitting off operation on graphs to binary matroids and investigate the relations between
the matroids resulting from this operation and the original binary matroids in terms of representation matrices, bases, rank
functions and connectivity. We also provide some interesting applications of this operation. 相似文献
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We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ. 相似文献
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在林寿与我最近合作的一篇文章中指出了∑^*-空间的构成定理需重新考虑.本文就是要证明在空间X的每个点是Gδ^-集的条件下该构成定理是成立的,所得的结论是:X是T1且每个点是Gδ^-集的∑^ -空间,如果f:X→Y是闭的满连续映射,则在Y中有-σ-闭离散子空间Z,使得对每个y∈Y\Z,f^-1(y)是X的ω1^-紧子空间.为得到该主要结果,本文证明了若空间X是每个点是Gδ^-集的次亚紧空间.则X中的每个闭离散子集是X中的Gδ^-集. 相似文献
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We introduce a special decomposition, the so-called split-minors, of the reduced clique graphs of chordal graphs. Using this notion, we characterize asteroidal sets in chordal graphs and clique trees with minimum number of leaves. 相似文献
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Carsten Thomassen 《Journal of Combinatorial Theory, Series B》1997,70(2):306-311
We give a simple proof of the fact (which follows from the Robertson–Seymour theory) that a graph which is minimal of genusgcannot contain a subdivision of a large grid. Combining this with the tree-width theorem and the quasi-wellordering of graphs of bounded tree-width in the Robertson–Seymour theory, we obtain a simpler proof of the generalized Kuratowski theorem for each fixed surface. The proof requires no previous knowledge of graph embeddings. 相似文献
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Let A be a central simple algebra over its center F. Define CK1 A = Coker(K1 F → K1 A). We prove that if A and B are F-central simple algebras of coprime degrees, then CK1(A? F B) = CK1 A × CK1 B. 相似文献
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一个矩阵称为稳定的,如果这个矩阵的特征值全包含在单位开圆盘内.利用Parker关于复方阵的分解定理给出了稳定矩阵分解定理的一个简单证明,并对奇异值全部严格小于1的矩阵给出了类似的结论. 相似文献
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Heinz König 《Positivity》2006,10(4):779-793
The decomposition theorem named after Lebesgue asserts that certain set functions have canonical representations as sums of
particular set functions called the absolutely continuous and the singular ones with respect to some fixed set function. The traditional versions are for the bounded measures with respect to some fixed measure on a σ algebra, in final form due to Hahn 1921, and for the bounded contents with respect to some fixed content on an algebra, due to Bochner-Phillips 1941 and Darst 1962. Then came the version
for arbitrary measures, due to R.A.Johnson 1967 and N.Y.Luther 1968. The unpleasant fact with these versions is that each one requires
its particular notions of absolutely continuous and singular constituents. It seems mysterious how a common roof for all of them could look, and therefore how a universal version for arbitrary contents could be achieved - and all that while several abstract extensions of particular versions appeared in the subsequent decades,
for example due to de Lucia-Morales 2003. After these decades now the present article claims to arrive at the final aim in
the original context of arbitrary contents. The article will be based on the author’s new difference formation for arbitrary contents 1999. This difference formation even furnishes simple explicit formulas for the two constituents.
Horst Tietz in alter Freundschaft gewidmet 相似文献
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R. Cordovil 《Discrete and Computational Geometry》2002,27(1):73-84
Let V be a vector space of dimension d over a field K and let A be a central arrangement of hyperplanes in V. To answer a question posed by K. Aomoto, P. Orlik and H. Terao construct a commutative K -algebra U(A) in terms of the equations for the hyperplanes of A. In the course of their work the following question naturally occurred:
\circ Is U(A) determined by the intersection lattice L(A) of the hyperplanes of A?
We give a negative answer to this question. The theory of oriented matroids gives rise to a combinatorial analogue of the
algebra of Orlik—Terao, which is the main tool of our proofs.
Received November 7, 2000, and in revised form May 18, 2001. Online publication November 2, 2001. 相似文献
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矩阵的秩分解定理是矩阵论中的一个基础性定理.本文给出了秩分解定理的一个证明,描述了其中可逆矩阵P,Q的构造,讨论了秩分解定理及其P,Q的构造在解线性方程组中的应用,以及在判别Sylvester不等式等号成立中的应用. 相似文献
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《随机分析与应用》2013,31(3):627-645
Abstract The notions of fuzzy random variables and fuzzy (super) submartingales are introduced. In this paper we provide the necessary and sufficient conditions of Doob's decomposition for fuzzy (super) submartingales. Finally, we discuss the decomposition of fuzzy (super) submartingales on R, and an example is given which explains that not every fuzzy (super) submartingale has Doob's decomposition. 相似文献