共查询到20条相似文献,搜索用时 15 毫秒
1.
P. Bowcock B. L. Feigin A. M. Semikhatov A. Taormina 《Communications in Mathematical Physics》2000,214(3):495-545
We discover a realisation of the affine Lie superalgebra and of the exceptional affine superalgebra as vertex operator extensions of two algebras with “dual” levels (and an auxiliary level-1 algebra). The duality relation between the levels is . We construct the representation of on a sum of tensor products of , , and modules
and decompose it into a direct sum over the spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction
to is traced to the properties of embeddings into and their relation with the dual pairs. Conversely, we show how the representations are constructed from representations.
Received: 29 July 1999 / Accepted: 6 February 2000 相似文献
2.
Haisheng Li 《Communications in Mathematical Physics》2001,217(3):653-696
We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras A
k
(sl(2)) for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible
modules are classified, complete reducibility of every module is proved and fusion rules are determined modulo the fusion
rules for vertex operator algebras of affine type.
Received: 7 March 2000 / Accepted: 10 November 2000 相似文献
3.
Oussama Hijazi Sebastián Montiel Xiao Zhang 《Communications in Mathematical Physics》2001,221(2):255-265
Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues
of the Dirac operator on compact spin manifolds with boundary. For the local boundary conditions, limiting cases are characterized
by the existence of real Killing spinors and the minimality of the boundary.
Received: 22 August 2000 / Accepted: 15 March 2001 相似文献
4.
It is well known that the Lie algebra structure on quantum algebras gives rise to a Poisson algebra structure on classical algebras as the Planck constant goes to 0. We show that this correspondence still holds in the generalization of superalgebra introduced by Scheunert, called -algebra. We illustrate this with the example of Number Operator Algebras, a new kind of object that we have defined and classified under some assumptions. 相似文献
5.
6.
T. A. Larsson 《Communications in Mathematical Physics》2000,214(2):469-491
Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra?DRO(N) be the extension of diff(N)⊕ diff(1) by its four inequivalent Virasoro-like cocycles. Here diff(N) is the diffeomorphism algebra in N-dimensional spacetime and diff(1) describes reparametrizations of trajectories in the space of tensor-valued p-jets. DRO(N) has a Fock module for each p and each representation of gl(N). Analogous representations for gauge algebras (higher-dimensional Kac–Moody algebras) are also given. The reparametrization
symmetry can be eliminated by a gauge fixing procedure, resulting in previously discovered modules. In this process, two DRO(N) cocycles transmute into anisotropic cocycles for diff(N). Thus the Fock modules of toroidal Lie algebras and their derivation algebras are geometrically explained.
Received: 29 October 1998 / Accepted: 2 May 2000 相似文献
7.
We extend our variant of mirror symmetry for K3 surfaces [GN3] and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models A and B) of Calabi-Yau manifolds fibrated by K3 surfaces with some special Picard lattices. These two classes are related with automorphic forms on IV type domains which we studied in our papers [GN1]-[GN6]. Conjecturally these automorphic forms take part in the quantum intersection pairing for model A, Yukawa coupling for model B and mirror symmetry between these two classes of Calabi-Yau manifolds. Recently there were several papers by physicists where it was shown on some examples. We propose a problem of classification of introduced Calabi-Yau manifolds. Our papers [GN1]-[GN6] and [N3]-[N14] give hope that this is possible. They describe possible Picard or transcendental lattices of general K3 fibers of the Calabi-Yau manifolds. 相似文献
8.
We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝ
n
. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global features.
The new examples include the instanton algebra and the NC-4-spheres S
4
θ. We construct the noncommutative algebras ?=C
∞ (S
4
θ) of functions on NC-spheres as solutions to the vanishing, ch
j
(e) = 0, j < 2, of the Chern character in the cyclic homology of ? of an idempotent e∈M
4 (?), e
2=e, e=e
*. We describe the universal noncommutative space obtained from this equation as a noncommutative Grassmannian as well as the
corresponding notion of admissible morphisms. This space Gr contains the suspension of a NC-3-sphere S
3
θ distinct from quantum group deformations SU
q
(2) of SU (2).
We then construct the noncommutative geometry of S
θ
4 as given by a spectral triple ?, ℋ, D) and check all axioms of noncommutative manifolds. In a previous paper it was shown that for any Riemannian metric g
μν on S
4 whose volume form is the same as the one for the round metric, the corresponding Dirac operator gives a solution to the following quartic equation,
where <␣> is the projection on the commutant of 4 × 4 matrices.
We shall show how to construct the Dirac operator D on the noncommutative 4-spheres S
θ
4 so that the previous equation continues to hold without any change.
Finally, we show that any compact Riemannian spin manifold whose isometry group has rank r≥ 2 admits isospectral deformations to noncommutative geometries.
Received: 5 December 2000 / Accepted: 8 March 2001 相似文献
9.
Friedrich Wagemann 《Communications in Mathematical Physics》1999,208(2):521-540
This article continues work of B. L. Feigin [5] and N. Kawazumi [15] on the Gelfand-Fuks cohomology of the Lie algebra of
holomorphic vector fields on a complex manifold. As this is not always an interesting Lie algebra (for example, it is 0 for
a compact Riemann surface of genus greater than 1), one looks for other objects having locally the same cohomology. The answer
is a cosimplicial Lie algebra and a differential graded Lie algebra (well known in Kodaira–Spencer deformation theory). We
calculate the corresponding cohomologies and the result is very similar to the result of A. Haefliger [12], R. Bott and G.
Segal [2] in the case of vector fields. Applications are in conformal field theory (for Riemann surfaces), deformation theory and foliation theory.
Received: 25 February 1999 / Accepted: 20 July 1999 相似文献
10.
Denis Perrot 《Communications in Mathematical Physics》2001,218(2):373-391
We consider a smooth groupoid of the form Σ⋊Γ, where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local
conformal diffeomorphisms. After defining a K-cycle on the crossed product C
0(Σ)⋊Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem
of Connes and Moscovici. This involves in particular a generalisation of the Euler class constructed from the modular automorphism
group of the von Neumann algebra L
∞(Σ)⋊Γ.
Received: 1 February 2000 / Accepted: 3 December 2000 相似文献
11.
We consider 1-D Schr?dinger operators on L
2(R
+) with slowly decaying potentials. Under some conditions on the potential, related to the first integrals of the KdV equation,
we prove that the a.c. spectrum of the operator coincides with the positive semiaxis and the singular spectrum is unstable.
Examples show that for special classes of sparse potentials these results can not be improved.
Received: 16 June 2000 / Accepted: 11 August 2000 相似文献
12.
We explain how to use a certain new Jacobi identity for vertex operator algebras, announced in a previous paper (math.QA/9909178), to interpret and generalize S. Bloch's recent work relating values of the Riemann zeta function at negative integers to a certain Lie algebra of operators. 相似文献
13.
14.
Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux–Egoroff
equations. This system of partial differential equations appears as a specific subset of the n-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions
of this Darboux–Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy
tau-function can be expressed in the KP tau-function.
Received: 1 September 1998 / Accepted: 7 March 1999 相似文献
15.
Andre Reznikov 《Communications in Mathematical Physics》2001,222(2):249-267
We consider the Laplace–Beltrami operator on a compact Riemann surface of a constant negative curvature. For any eigenvalue
of the Laplace–Beltrami operator there is an associated sequence of measures on the Riemann surface. These measures naturally
appear in Quantum Chaos type questions in the theory of electro-magnetic flow on a Riemann surface. The main result of the
paper is the claim that this sequence of measures has the Liouville measure as the (weak*) limit. We prove a quantitative version of this equidistribution claim.
Received: 12 March 2001 / Accepted: 23 April 2001 相似文献
16.
For Seifert homology spheres, we derive a holomorphic function of K whose value at integer K is the sl
2 Witten–Reshetikhin–Turaev invariant, Z
K
, at q= exp 2πi/K. This function is expressed as a sum of terms, which can be naturally corresponded to the contributions of flat connections
in the stationary phase expansion of the Witten–Chern–Simons path integral. The trivial connection contribution is found to
have an asymptotic expansion in powers of K
−1 which, for K an odd prime power, converges K-adically to the exact total value of the invariant Z
K
at that root of unity. Evaluations at rational $K$ are also discussed. Using similar techniques, an expression for the coloured
Jones polynomial of a torus knot is obtained, providing a trivial
connection contribution which is an analytic function of the colour. This demonstrates that the stationary phase expansion
of the Chern–Simons–Witten theory is exact for Seifert manifolds and for torus knots in S
3. The possibility of generalising such results is also discussed.
Received: 26 October 1998 / Accepted: 1 March 1999 相似文献
17.
Roberto Peirone 《Communications in Mathematical Physics》1999,207(1):67-80
I prove that in (sufficiently small) tubular ρ$-neighborhoods of a given C
3 manifold of codimension 1, any two points can be connected by a billiard trajectory, and that in addition there exists such
a trajectory having at most collision points, for a suitable H>0, provided the manifold is of class C
3.
Received: 19 June 1998 / Accepted: 7 April 1999 相似文献
18.
The moduli space ${\mathcal {NK}}The moduli space NK{\mathcal {NK}} of infinitesimal deformations of a nearly K?hler structure on a compact 6-dimensional manifold is described by a certain
eigenspace of the Laplace operator acting on co-closed primitive (1, 1) forms (cf. Moroianu et al. in Pacific J Math 235:57–72,
2008). Using the Hermitian Laplace operator and some representation theory, we compute the space NK{\mathcal {NK}} on all 6-dimensional homogeneous nearly K?hler manifolds. It turns out that the nearly K?hler structure is rigid except for
the flag manifold F(1, 2) = SU3/T
2, which carries an 8-dimensional moduli space of infinitesimal nearly K?hler deformations, modeled on the Lie algebra
\mathfraksu3{\mathfrak{su}_3} of the isometry group. 相似文献
19.
We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial
algebra endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the
semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary
we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier.
This research of the first author was supported by a Marie Curie Intra-European Fellowship within the 6th European Community
Framework Programme. The second author was supported by EPSRC Grant EP/D034167/1. 相似文献
20.
Pedro Freitas 《Communications in Mathematical Physics》2001,217(2):375-382
We consider the problem of minimizing the eigenvalues of the Schr?dinger operator H=−Δ+αF(κ) (α>0) on a compact n-manifold subject to the restriction that κ has a given fixed average κ0.
In the one-dimensional case our results imply in particular that for F(κ)=κ2 the constant potential fails to minimize the principal eigenvalue for α>αc=μ1/(4κ0
2), where μ1 is the first nonzero eigenvalue of −Δ. This complements a result by Exner, Harrell and Loss, showing that the critical value
where the constant potential stops being a minimizer for a class of Schr?dinger operators penalized by curvature is given
by α
c
. Furthermore, we show that the value of μ1/4 remains the infimum for all α >α
c
. Using these results, we obtain a sharp lower bound for the principal eigenvalue for a general potential.
In higher dimensions we prove a (weak) local version of these results for a general class of potentials F(κ), and then show that globally the infimum for the first and also for higher eigenvalues is actually given by the corresponding
eigenvalues of the Laplace–Beltrami operator and is never attained.
Received: 17 July 2000 / Accepted: 11 October 2000 相似文献