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61.
Alexander I. Shtern 《Acta Appl Math》2001,68(1-3):105-121
We present a brief review of the theory of quasi-characters and quasi-representations and prove a necessary and sufficient condition that the second real continuous bounded cohomology of a locally compact group to be finite-dimensional. This criterion is established by using the properties of continuous pseudocharacters on a locally compact group. 相似文献
62.
The paper provides a combinatorial method to decide when the space of local systems with nonvanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of positive dimension. Partial classification of arrangements having such a component of positive dimension and a comparison theorem for cohomology of Orlik–Solomon algebra and cohomology of local systems are given. The methods are based on Vinberg–Kac classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components. 相似文献
63.
Aliaa Barakat 《Advances in Mathematics》2008,219(2):604-632
We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative ∂u of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group. 相似文献
64.
考虑具有导子的李三系.由李三系和一个导子称为LietsDer对.定义系数在表示中的LietsDer对的上同调理论.研究LietsDer对的中心扩张.接下来,将形变理论推广到由李三系和导子构成LietsDer对上,它由带有系数的LietsDer对的上同调所支配. 相似文献
65.
We explicitly compute the first and second cohomology groups of the Schrdinger algebra S(1) with coefficients in the trivial module and the finite-dimensional irreducible modules.We also show that the first and second cohomology groups of S(1) with coefficients in the universal enveloping algebras U(S(1))(under the adjoint action) are infinite dimensional. 相似文献
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69.
We prove that for smooth surfaces over real closed fields, and a class of smooth projective surfaces over a real number field, the map between mod 2 algebraic and étale K-theory is an isomorphism in sufficiently large degrees. For a class of smooth projective surfaces over a real closed field, including rational surfaces, complete intersections and K3-surfaces over the real numbers, we explicate the abutment of the mod 2 motivic cohomology to algebraic K-theory spectral sequence. 相似文献
70.
Wiesł Nizioł 《Compositio Mathematica》2001,129(2):123-147
We define and study a candidate for 'arithmetic' cohomology theory with values in crystalline p-adic smooth sheaves. We show that it injects into arithmetic étale cohomology and prove a duality result. 相似文献