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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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With any -manifold M are associated two dglas and , whose cohomologies and are Gerstenhaber algebras. We establish a formality theorem for -manifolds: there exists an quasi-isomorphism whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the -manifold M, and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the -manifold M is an isomorphism of Gerstenhaber algebras from to . 相似文献
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W. Frank Moore 《Journal of Algebra》2009,321(3):758-773
Let S and T be local rings with common residue field k, let R be the fiber product , and let M be an S-module. The Poincaré series of M has been expressed in terms of , and by Kostrikin and Shafarevich, and by Dress and Krämer. Here, an explicit minimal resolution, as well as theorems on the structure of and are given that illuminate these equalities. Structure theorems for the cohomology modules of fiber products of modules are also given. As an application of these results, we compute the depth of cohomology modules over a fiber product. 相似文献
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《Comptes Rendus Mathematique》2005,340(12):885-888
This Note presents a randomized method to approximate any vector v from some set . The data one is given is the set T, and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability any for which is close to the data vector will be a good approximation of v, and that the degree of approximation is determined by a natural geometric parameter associated with the set T. This extends and improves recent results by Candes and Tao. To cite this article: S. Mendelson et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). 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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Djagwa Dehainsala 《Comptes Rendus Mathematique》2009,347(23-24):1419-1422
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In this paper we determine the projective unitary representations of finite dimensional Lie supergroups whose underlying Lie superalgebra is , where is a compact simple Lie superalgebra and A is a supercommutative associative (super)algebra; the crucial case is when is a Graßmann algebra. Since we are interested in projective representations, the first step consists in determining the cocycles defining the corresponding central extensions. Our second main result asserts that, if is a simple compact Lie superalgebra with , then each (projective) unitary representation of factors through a (projective) unitary representation of itself, and these are known by Jakobsen's classification. If , then we likewise reduce the classification problem to semidirect products of compact Lie groups K with a Clifford–Lie supergroup which has been studied by Carmeli, Cassinelli, Toigo and Varadarajan. 相似文献