共查询到20条相似文献,搜索用时 54 毫秒
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多复变在非交换非结合领域的推广近年来取得了迅猛的发展.本文简单介绍这方面的最新进展,其中包括切片Clifford分析、离散Clifford分析、Hermitian Clifford分析、Dunkl Clifford分析、四元数分析、八元数分析,离散复分析在统计物理中Ising模型的应用,以及与切片Clifford分析相关的S-谱理论在量子物理的应用. 相似文献
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本文研究了非自伴Dirac算子的一般两点边值问题的渐近迹,首先运用平移算子得到了其Cauchy问题解的渐近式,并由此及边界条件,构造了整函数ω(λ),利用它将边界条件分为八种基本类型,最后采用留数的方法,得到了四种主要类型的特征值的渐近迹公式。 相似文献
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用Lafferty等人的几何方法给出了奇数维旋流形上定向反转的反演的Freed的Lefschetz不动点公式的一个证明,然后将这个公式推广到了非交换几何框架. 相似文献
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交换整环上的上三角矩阵保对合的线性算子 总被引:1,自引:0,他引:1
本文刻划了交换整环R上的上三角长阵的R-代数Fn(R)的保对合的可逆线性算子,由此又确定了Fn(R)的保立方幂等的可逆线性算子。 相似文献
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关于Gross问题的一个注记 总被引:6,自引:0,他引:6
本文研究亚纯函数的唯一性,得到了如下结果.设S={z:z3-z2-1=0},f(z)与g(z)是满足Θ(∞,f)>12,Θ(∞,g)>12,的两个非常数亚纯函数.若E(0,f)=E(0,g),E(S,f)=E(S,g)以及E(∞,f)=E(∞,g),则f(z)≡g(z).这个结果彻底解决了Gross[3]于1976年提出的一个问题 相似文献
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本文给出了双侧加权移位算子的近次正常性的完全刻画.作为主要结果的应用,文章的最后提供了Hilbert空间第160问题的许多新的答案. 相似文献
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Let P be an isolated singularity of multiplicity 4 of a complex surface Y. It is well-known that there is a locally irreducible finite covering π:(Y, P) → (X, p) with π-1(p)=P, and a Jung's resolution f:Ỹ → Y. Let Wp be the exceptional divisor of (π◦f)-1(p). We will prove that Wp has a unique decomposition into fundamental cycles Wp=2Z1 or Wp=Σα=1l Zα satisfying some conditions. We will define a local index wp for π at p and compute it by the above decomposition of Wp. In particular, we will show that (Y, P) is singular iff wp ≥ 1. As another application of the decomposition of Wp, we also compute the number of blown-downs needed to get the minimal resolution from Ỹ. © 2021, Chinese Academy of Sciences. All right reserved. 相似文献
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Fangbing Wu 《K-Theory》1993,7(2):145-174
A cyclic cocycle is constructed for the Dirac operator on a compact spin manifold with boundary with the -invariant cochain introduced as the boundary correction term. This cocycle is seen to satisfy certain growth condition weaker than being entire and its pairing with the Chern characters of idempotents as well as the relevant index formulae are studied. The -cochain is a generalization of the Atiyah-Patodi-Singer -invariant and it carries information on the APS -invariants for Dirac operators twisted by bundles. It is also shown that one obtains the transgressed Chern character, defined by Connes and Moscovici, by applying the boundary operatorB in the cyclic bicomplex to the higher components of the -cochain. 相似文献
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Victor Nistor 《K-Theory》1991,5(3):193-211
We define a Chern character for p-summable quasihomomorphisms. We study its properties and show that it is compatible with the analytic index. The results are similar to Connes' results on the Chern character on K-homology but the methods are different. This solves most of a problem of Connes. 相似文献
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For the action of a locally compact and totally disconnected group G on a pair of locally compact spaces X and Y we construct, by sheaf theoretic means, a new equivariant and bivariant cohomology theory. If we take for the first space Y an universal proper G-action then we obtain for the second space its delocalized equivariant homology. This is in exact formal analogy to the definition of equivariant K-homology by Baum, Connes, Higson starting from the bivariant equivariant Kasparov KK-theory. Under certain basic finiteness conditions on the first space Y we conjecture the existence of a Chern character from the equivariant Kasparov KK-theory of Y and X into our cohomology theory made two-periodic which becomes an isomorphism upon tensoring the KK-theory with the complex numbers. This conjecture is proved for profinite groups G. An essential role in our construction is played by a bivariant version of Segal localization which we establish for KK-theory. 相似文献
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Alexander Gorokhovsky 《Journal of Functional Analysis》2006,237(1):105-134
In this paper we consider a family of Dirac-type operators on fibration P→B equivariant with respect to an action of an étale groupoid. Such a family defines an element in the bivariant K theory. We compute the action of the bivariant Chern character of this element on the image of Connes' map Φ in the cyclic cohomology. A particular case of this result is Connes' index theorem for étale groupoids [A. Connes, Noncommutative Geometry, Academic Press, 1994] in the case of fibrations. 相似文献
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Let be a connected semisimple Lie group with finite center. Let be the maximal compact subgroup of corresponding to a fixed Cartan involution . We prove a conjecture of Vogan which says that if the Dirac cohomology of an irreducible unitary -module contains a -type with highest weight , then has infinitesimal character . Here is the half sum of the compact positive roots. As an application of the main result we classify irreducible unitary -modules with non-zero Dirac cohomology, provided has a strongly regular infinitesimal character. We also mention a generalization to the setting of Kostant's cubic Dirac operator.
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In this paper we research the lower bound of the eigenvalue of Spinc Dirac operator on the Spinc manifold. By the Weisenbock formula, we get an estimate of it, then following the idea of Th Friedrich [2] and X Zhang [6]. We get a finer estimate of it. As an application, we give a condition when the Seiberg-Witten equation only has 0 solution. 相似文献
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We give optimal lower bounds for the hypersurface Diracoperator in terms of the Yamabe number, the energy-momentum tensor andthe mean curvature. In the limiting case, we prove that the hypersurfaceis an Einstein manifold with constant mean curvature. 相似文献
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In this paper we generalize the results of Part I to the submanifoldDirac operator. In particular, we give optimal lower bounds for thesubmanifold Dirac operator in terms of the mean curvature and othergeometric invariants as the Yamabe number or the energy-momentum tensor.In the limiting case, we prove that the submanifold is Einstein if thenormal bundle is flat. 相似文献
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For an algebra
with an action of a Hopf algebra
we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for
. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space
for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg's theorem relating
equivariant K-theory to ordinary K-theory of the C*-algebra crossed product, and characterize equivariant vector bundles on quantum homogeneous spaces. 相似文献