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We give a characterization of exponentiable monomorphisms in the categories of ω-complete posets, of directed complete posets and of continuous directed complete posets as those monotone maps f that are convex and that lift an element (and then a queue) of any directed set (ω-chain in the case of ) whose supremum is in the image of f (Theorem 1.9). Using this characterization, we obtain that a monomorphism f:X→B in (, ) exponentiable in w.r.t. the Scott topology is exponentiable also in (, ). We prove that the converse is true in the category , but neither in , nor in . 相似文献
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We show that the π-equivariant chain complex (), , associated to a Morse-theoretic minimal CW-structure X on the complement of an arrangement , is independent of X. The same holds for all scalar extensions, , a field, where X is an arbitrary minimal CW-structure on a space M. When is a section of another arrangement , we show that the divisibility properties of the first Betti number of the Milnor fiber of obstruct the homotopy realization of as a subcomplex of a minimal structure on .If is aspherical and is a sufficiently generic section of , then may be described in terms of π, L and , for an arbitrary local system L; explicit computations may be done, when is fiber-type. In this case, explicit -presentations of arbitrary abelian scalar extensions of the first non-trivial higher homotopy group of , πp(M), may also be obtained. For nonresonant abelian scalar extensions, the -rank of is combinatorially determined. 相似文献
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Eli Aljadeff 《Advances in Mathematics》2008,218(5):1453-1495
To any cleft Hopf Galois object, i.e., any algebra obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle α, we attach two “universal algebras” and . The algebra is obtained by twisting the multiplication of H with the most general two-cocycle σ formally cohomologous to α. The cocycle σ takes values in the field of rational functions on H. By construction, is a cleft H-Galois extension of a “big” commutative algebra . Any “form” of can be obtained from by a specialization of and vice versa. If the algebra is simple, then is an Azumaya algebra with center . The algebra is constructed using a general theory of polynomial identities that we set up for arbitrary comodule algebras; it is the universal comodule algebra in which all comodule algebra identities of are satisfied. We construct an embedding of into ; this embedding maps the center of into when the algebra is simple. In this case, under an additional assumption, , thus turning into a central localization of . We completely work out these constructions in the case of the four-dimensional Sweedler algebra. 相似文献
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Tomoyoshi Ohwada Guoxing Ji Atsushi Hasegawa 《Journal of Mathematical Analysis and Applications》2006,315(1):216-224
Let G be a compact abelian group with the totally ordered dual group which admits the positive semigroup . Let N be a von Neumann algebra and be an automorphism group of on N. We denote to the analytic crossed product determined by N and α. We show that if is a maximal σ-weakly closed subalgebra of , then induces an archimedean order in . 相似文献
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Mitsuru Uchiyama 《Journal of Functional Analysis》2006,231(1):221-244
Let P+ be the set of all non-negative operator monotone functions defined on [0,∞), and put . Then and . For a function and a strictly increasing function h we write if is operator monotone. If and and if and , then . We will apply this result to polynomials and operator inequalities. Let and be non-increasing sequences, and put for t≧a1 and for t≧b1. Then v+?u+ if m≦n and : in particular, for a sequence of orthonormal polynomials, (pn-1)+?(pn)+. Suppose 0<r,p and s=0 or 1≦s≦1+p/r. Then 0≦A≦B implies for 0<α≦r/(p+r). 相似文献
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Xiang-dong Hou 《Journal of Combinatorial Theory, Series A》2007,114(3):522-544
Let Ψn be the number of inequivalent self-dual codes in . We prove that , where . Let Δn be the number of inequivalent doubly even self-dual codes in . We also prove that . 相似文献
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Let γ be the Gauss measure on and the Ornstein-Uhlenbeck operator. For every p in [1,∞)?{2}, set , and consider the sector . The main results of this paper are the following. If p is in (1,∞)?{2}, and , i.e., if M is an Lp(γ)uniform spectral multiplier of in our terminology, and M is continuous on , then M extends to a bounded holomorphic function on the sector . Furthermore, if p=1 a spectral multiplier M, continuous on , satisfies the condition if and only if M extends to a bounded holomorphic function on the right half-plane, and its boundary value M(i·) on the imaginary axis is the Euclidean Fourier transform of a finite Borel measure on the real line. We prove similar results for uniform spectral multipliers of second order elliptic differential operators in divergence form on belonging to a wide class, which contains . From these results we deduce that operators in this class do not admit an H∞ functional calculus in sectors smaller than . 相似文献
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Dragomir Šari? 《Topology》2005,44(1):99-130
Consider a hyperbolic surface X of infinite area. The Liouville map assigns to any quasiconformal deformation of X a measure on the space of geodesics of the universal covering X? of X. We show that the Liouville map is a homeomorphism from the Teichmüller space onto its image, and that the image is closed and unbounded. The set of asymptotic rays to consists of all bounded measured laminations on X. Hence, the set of projective bounded measured laminations is a natural boundary for . The action of the quasiconformal mapping class group on continuously extends to this boundary for . 相似文献
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Let be the anticipating smooth semimartingale and be its generalized local time. In this paper, we give some estimates about the quasi sure property of Xt and its quadratic variation process t〈X〉. We also study the fractional smoothness of and prove that the quadratic variation process of can be constructed as the quasi sure limit of the form , where is a sequence of subdivisions of [a,b], , i=0,1,…,n2. 相似文献
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Janez Mr?un 《Journal of Pure and Applied Algebra》2007,210(1):267-282
For any étale Lie groupoid G over a smooth manifold M, the groupoid convolution algebra of smooth functions with compact support on G has a natural coalgebra structure over the commutative algebra which makes it into a Hopf algebroid. Conversely, for any Hopf algebroid A over we construct the associated spectral étale Lie groupoid over M such that is naturally isomorphic to G. Both these constructions are functorial, and is fully faithful left adjoint to . We give explicit conditions under which a Hopf algebroid is isomorphic to the Hopf algebroid of an étale Lie groupoid G. 相似文献
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Special Transverse Slices and Their Enveloping Algebras 总被引:1,自引:0,他引:1
Alexander Premet 《Advances in Mathematics》2002,170(1):1-55
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Zhi-Hong Sun 《Journal of Number Theory》2005,113(1):10-52
Let be a prime, m∈Z and . In this paper we obtain a general criterion for m to be a quartic residue in terms of appropriate binary quadratic forms. Let d>1 be a squarefree integer such that , where is the Legendre symbol, and let εd be the fundamental unit of the quadratic field . Since 1942 many mathematicians tried to characterize those primes p so that εd is a quadratic or quartic residue . In this paper we will completely solve these open problems by determining the value of , where p is an odd prime, and . As an application we also obtain a general criterion for , where {un(a,b)} is the Lucas sequence defined by and . 相似文献