共查询到20条相似文献,搜索用时 31 毫秒
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Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by and , respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthly 83 (1976) 265–266], for any graph G, . The first counterexample to this conjecture was obtained by Alon and Seymour [J. Graph Theor. 13 (1989) 523–525]. Recently, Fishkind and Kotlov [Discrete Math. 250 (2002) 253–257] have proved that for any graph G, . In this Note we improve Fishkind–Kotlov upper bound and show that . To cite this article: S. Akbari, H.-R. Fanaï, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Dave Anderson Mathieu Florence Zinovy Reichstein 《Comptes Rendus Mathematique》2013,351(23-24):871-875
Let G be a split simple group of type over a field k, and let be its Lie algebra. Answering a question of J.-L. Colliot-Thélène, B. Kunyavski?, V.L. Popov, and Z. Reichstein, we show that the function field is generated by algebraically independent elements over the field of adjoint invariants . 相似文献
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We classify the 6-dimensional Lie algebras of the form that admit an integrable complex structure. We also endow a Lie algebra of the kind () with such a complex structure. The motivation comes from geometric structures à la Sasaki on -manifolds. 相似文献
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Let A be an Abelian variety defined over a number field k. Let P be a point in and let X be a subgroup of . Gajda and Kowalski asked in 2002 whether it is true that the point P belongs to X if and only if the point belongs to for all but finitely many primes of k. We provide a counterexample. 相似文献
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Let G be a complex linear algebraic group, its Lie algebra and a nilpotent element. Vust's Theorem says that in case of , the algebra , where is the stabilizer of e under the adjoint action, is generated by the image of the natural action of d-th symmetric group and the linear maps . In this paper, we give an analogue of Vust's Theorem for and when the nilpotent elements e satisfy that is normal. As an application, we study the higher Schur–Weyl duality in the sense of [4] for types B, C and D, which establishes a relationship between W-algebras and degenerate affine braid algebras. 相似文献
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Ilya Shapiro 《Advances in Mathematics》2009,220(6):1657-1688
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Pham Hung Quy 《Journal of Pure and Applied Algebra》2018,222(5):1126-1138
Let be an equidimensional excellent local ring of characteristic . The aim of this paper is to show that does not depend on the choice of parameter ideal provided R is an F-injective local ring that is F-rational on the punctured spectrum. 相似文献
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Given a local domain of prime characteristic that is a homomorphic image of a Gorenstein ring, Huneke and Lyubeznik proved that there exists a module-finite extension domain S such that the induced map on local cohomology modules is zero for each . We prove that the extension S may be chosen to be generically Galois, and analyze the Galois groups that arise. 相似文献