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1.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
2.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 相似文献
3.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
4.
We show that there are canonical isomorphisms between Hochschild cohomology spaces
, where
is the algebra of smooth functions on a manifold M and
the space of skew multivector fields over M. This implies that continuous and differential deformation theories of
coincide. 相似文献
5.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
6.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
7.
In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators
. The reduction of the Poisson structure to the symplectic submanifold
gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as
, where
means the multiplicity of roots and to the case (b) is defined by
where
is the multiplicity of poles. We prove that
-algebra is isomorphic via a transformation to
U(1) with m=
. We also give the explicit free fields representations for these W-algebras. 相似文献
8.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
9.
The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that
being the height of the current algebra representation) acts in
-dimensional indefinite metric space
of quantum group invariant vectors. The generalized cohomologies Ker
are 1-dimensional. Their direct sum spans the physical subquotient of
. 相似文献
10.
A simplified construction of representations is presented for the quantized enveloping algebra
q (
), with
being a simple complex Lie algebra belonging to one of the four principal series A\ell, B\ell, C\ell or D\ell. The carrier representation space is the quantized algebra of polynomials in antiholomorphic coordinate functions on the big cell of a coadjoint orbit of K where K is the compact simple Lie group with the Lie algebra
– the compact form of
. 相似文献
11.
Given a braided vector space
, we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on
. Using the quantum shuffle construction of the 'upper triangular part'
of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of
. 相似文献
12.
Let
be von Neumann algebras acting on a Hilbert space
and let
be a common cyclic and separating vector. We say that
have the modular intersection property with respect to
if(1)
-half-sided modular inclusions,(2)
(If (1) holds the strong limit exists.) We show that under these conditions the modular groups of
and
generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2,
)/Z
2 generated by modular groups. 相似文献
13.
We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let
be a fixed Lie algebra. We shall say that a Kontsevich star product is
-relative if, on
*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if
is a semi-simple Lie algebra, the only strict Kontsevich
-relative star products are the relative (for every Lie algebras) Kontsevich star products. 相似文献
14.
We derive explicit formulas for the multipoint series of
in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of
. We also obtain explicit formulas for the Hodge integrals
, in the cases i=0 and 1. 相似文献
15.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献
16.
This Letter concerns an extension of the quantum spinor construction of
. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and construct quantum spinor representations of
. 相似文献
17.
Let A, B be positive operators on a Hilbert space, z any complex number, m any positive integer, and
any unitarily invariant norm. We show that
and
Some related inequalities are also obtained. 相似文献
18.
We consider the Dirichlet Laplacian for astrip in
with one straight boundary and a width
, where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase,
, the operator has nobound statesfor small
.On the otherhand, a weakly bound state existsprovided
. In thatcase, there are positive c
1,c
2 suchthat the corresponding eigenvalue satisfies
for all
sufficiently small. 相似文献
19.
20.
We construct embeddings of boundary algebras
into ZF algebras
. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for
and without for
), this connection allows to make the link between different approaches of the systems with boundaries. The construction uses the well-bred vertex operators built recently, and is classified by reflection matrices. It relies only on the existence of an R-matrix obeying a unitarity condition, and as such can be applied to any infinite dimensional quantum group. 相似文献