共查询到20条相似文献,搜索用时 22 毫秒
1.
This paper studies the twisted representations of vertex operator algebras. Let be a vertex operator algebra and an automorphism of of finite order For any , an - -bimodule is constructed. The collection of these bimodules determines any admissible -twisted -module completely. A Verma type admissible -twisted -module is constructed naturally from any -module. Furthermore, it is shown with the help of bimodule theory that a simple vertex operator algebra is -rational if and only if its twisted associative algebra is semisimple and each irreducible admissible -twisted -module is ordinary. 相似文献
2.
Let be a finite abelian group. We will consider a skew product extension of a product of two Cantor minimal -systems associated with a -valued cocycle. When is non-cyclic and the cocycle is non-degenerate, it will be shown that the skew product system has torsion in its coinvariants. 相似文献
3.
For an odd prime, we generalise the Glauberman-Thompson -nilpotency theorem (Gorenstein, 1980) to arbitrary fusion systems. We define a notion of -free fusion systems and show that if is a -free fusion system on some finite -group , then is controlled by for any Glauberman functor , generalising Glauberman's -theorem (Glauberman, 1968) to arbitrary fusion systems. 相似文献
4.
This paper provides a topological method to construct all simply-connected, spin, smooth -manifolds with torsion-free homology using simply-connected, smooth -manifolds as building blocks. We explicitly determine the invariants that classify these -manifolds from the intersection form and specific homology classes of the -manifold building blocks. 相似文献
5.
Operators of the form with a pseudodifferential symbol belonging to the Hörmander class , , , and certain perturbations are shown to possess a bounded -calculus in Besov-Triebel-Lizorkin and certain subspaces of Hölder spaces, provided is suitably elliptic. Applications concern pseudodifferential operators with mildly regular symbols and operators on manifolds of low regularity. An example is the Dirichlet-Neumann operator for a compact domain with -boundary. 相似文献
6.
Let be a field of characteristic not whose virtual cohomological dimension is at most . Let be a semisimple group of adjoint type defined over . Let denote the normal subgroup of consisting of elements -equivalent to identity. We show that if is of classical type not containing a factor of type , . If is a simple classical adjoint group of type , we show that if and its multi-quadratic extensions satisfy strong approximation property, then . This leads to a new proof of the -triviality of -rational points of adjoint classical groups defined over number fields. 相似文献
7.
A -local finite group consists of a finite -group , together with a pair of categories which encode ``conjugacy' relations among subgroups of , and which are modelled on the fusion in a Sylow -subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as -completed classifying spaces of finite groups. In this paper, we study and classify extensions of -local finite groups, and also compute the fundamental group of the classifying space of a -local finite group. 相似文献
8.
Let denote the Beurling-Ahlfors transform defined on , . The celebrated conjecture of T. Iwaniec states that its norm where . In this paper the new upper estimate is found. 相似文献
9.
We prove that structure constants related to Hecke algebras at roots of unity are special cases of -Littlewood-Richardson coefficients associated to a product of -Schur functions. As a consequence, both the 3-point Gromov-Witten invariants appearing in the quantum cohomology of the Grassmannian, and the fusion coefficients for the WZW conformal field theories associated to are shown to be -Littlewood-Richardson coefficients. From this, Mark Shimozono conjectured that the -Schur functions form the Schubert basis for the homology of the loop Grassmannian, whereas -Schur coproducts correspond to the integral cohomology of the loop Grassmannian. We introduce dual -Schur functions defined on weights of -tableaux that, given Shimozono's conjecture, form the Schubert basis for the cohomology of the loop Grassmannian. We derive several properties of these functions that extend those of skew Schur functions. 相似文献
10.
Say that a separable, unital -algebra is strongly self-absorbing if there exists an isomorphism such that and are approximately unitarily equivalent -homomorphisms. We study this class of algebras, which includes the Cuntz algebras , , the UHF algebras of infinite type, the Jiang-Su algebra and tensor products of with UHF algebras of infinite type. Given a strongly self-absorbing -algebra we characterise when a separable -algebra absorbs tensorially (i.e., is -stable), and prove closure properties for the class of separable -stable -algebras. Finally, we compute the possible -groups and prove a number of classification results which suggest that the examples listed above are the only strongly self-absorbing -algebras. 相似文献
11.
Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube and the -coarse category of their complements. The -coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants of Z-sets to the geometry of their complements. 相似文献
12.
We strengthen and generalise a result of Kirsch and Simon on the behaviour of the function , the number of bound states of the operator in below . Here is a bounded potential behaving asymptotically like where is a function on the sphere. It is well known that the eigenvalues of such an operator are all nonpositive, and accumulate only at 0. If the operator on the sphere has negative eigenvalues less than , we prove that may be estimated as Thus, in particular, if there are no such negative eigenvalues, then has a finite discrete spectrum. Moreover, under some additional assumptions including the fact that and that there is exactly one eigenvalue less than , with all others , we show that the negative spectrum is asymptotic to a geometric progression with ratio . 相似文献
13.
We show that, for each , there is an -tensor norm (in the sense of Grothendieck) with the surprising property that the -tensor product has local unconditional structure for each choice of arbitrary -spaces . In fact, is the tensor norm associated to the ideal of multiple -summing -linear forms on Banach spaces. 相似文献
14.
For , a one-parameter family of symmetric quantum derivatives is defined for each order of differentiation as are two families of Riemann symmetric quantum derivatives. For , symmetrization holds, that is, whenever the th Peano derivative exists at a point, all of these derivatives of order also exist at that point. The main result, desymmetrization, is that conversely, for , each symmetric quantum derivative is a.e. equivalent to the Peano derivative of the same order. For and , each th symmetric quantum derivative coincides with both corresponding th Riemann symmetric quantum derivatives, so, in particular, for and , both th Riemann symmetric quantum derivatives are a.e. equivalent to the Peano derivative. 相似文献
15.
The mapping class group of an oriented surface of genus with one boundary component has a natural decreasing filtration , where is the kernel of the action of on the nilpotent quotient of . Using a tree Lie algebra approximating the graded Lie algebra we prove that any integral homology sphere of dimension has for some a Heegaard decomposition of the form , where and is such that . This proves a conjecture due to S. Morita and shows that the ``core' of the Casson invariant is indeed the Casson invariant. 相似文献
16.
The three quantifier theory of , the recursively enumerable degrees under Turing reducibility, was proven undecidable by Lempp, Nies and Slaman (1998). The two quantifier theory includes the lattice embedding problem and its decidability is a long-standing open question. A negative solution to this problem seems out of reach of the standard methods of interpretation of theories because the language is relational. We prove the undecidability of a fragment of the theory of that lies between the two and three quantifier theories with but includes function symbols. Theorem. The two quantifier theory of , the r.e. degrees with Turing reducibility, supremum and infimum (taken to be any total function extending the infimum relation on ) is undecidable. The same result holds for various lattices of ideals of which are natural extensions of preserving join and infimum when it exits. 相似文献
17.
Let be a semi-simple connected Lie group. Let be a maximal compact subgroup of and the complexified Lie algebra of . In this paper we describe the center of the category of -modules. 相似文献
18.
Let be a compact connected Lie group, and a Hamiltonian -space with proper moment map . We give a surjectivity result which expresses the -theory of the symplectic quotient in terms of the equivariant -theory of the original manifold , under certain technical conditions on . This result is a natural -theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry. The main technical tool is the -theoretic Atiyah-Bott lemma, which plays a fundamental role in the symplectic geometry of Hamiltonian -spaces. We discuss this lemma in detail and highlight the differences between the -theory and rational cohomology versions of this lemma. We also introduce a -theoretic version of equivariant formality and prove that when the fundamental group of is torsion-free, every compact Hamiltonian -space is equivariantly formal. Under these conditions, the forgetful map is surjective, and thus every complex vector bundle admits a stable equivariant structure. Furthermore, by considering complex line bundles, we show that every integral cohomology class in admits an equivariant extension in . 相似文献
19.
Let be a regular ring, essentially of finite type over a perfect field . An -module is called a unit -module if it comes equipped with an isomorphism , where denotes the Frobenius map on , and is the associated pullback functor. It is well known that then carries a natural -module structure. In this paper we investigate the relation between the unit -structure and the induced -structure on . In particular, it is shown that if is algebraically closed and is a simple finitely generated unit -module, then it is also simple as a -module. An example showing the necessity of being algebraically closed is also given. 相似文献
20.
Let be a simple algebraic group over the complex numbers containing a Borel subgroup . Given a -stable ideal in the nilradical of the Lie algebra of , we define natural numbers which we call ideal exponents. We then propose two conjectures where these exponents arise, proving these conjectures in types and some other types. When , we recover the usual exponents of by Kostant (1959), and one of our conjectures reduces to a well-known factorization of the Poincaré polynomial of the Weyl group. The other conjecture reduces to a well-known result of Arnold-Brieskorn on the factorization of the characteristic polynomial of the corresponding Coxeter hyperplane arrangement. 相似文献
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