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1.
B. Enriquez 《Communications in Mathematical Physics》1995,170(1):197-206
We propose a quantum lattice version of B. Feigin and E. Frenkel's constructions, identifying the KdV differential polynomials with functions on a homogeneous space under the nilpotent part of
. We construct an action of the nilpotent part
of
on their lattice counterparts, and embed the lattice variables in a
, coinduced from a quantum version of the principal commutative subalgebra, which is defined using the identification of
with its dual algebra. 相似文献
2.
Ruedi Suter 《Communications in Mathematical Physics》1994,163(2):359-393
The restricted quantum universal enveloping algebra
decomposes in a canonical way into a direct sum of indecomposable left (or right) ideals. They are useful for determining the direct summands which occur in the tensor product of two simple
. The indecomposable finite-dimensional
are classified and located in the Auslander-Reiten quiver. 相似文献
3.
José M. Figueroa-O'Farrill 《Communications in Mathematical Physics》1996,177(1):129-156
Let
be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if
is self-dual (that is, if it possesses an invariant metric) then it admits anN=1 (affine) Sugawara construction. Under certain additional hypotheses, thisN=1 structure admits anN=2 extension. If this is the case,
is said to possess anN=2 structure. It is also known that anN=2 structure on a self-dual Lie algebra
is equivalent to a vector space decomposition
, where
are isotropic Lie subalgebras. In other words,N=2 structures on
in one-to-one correspondence with Manin triples
. In this paper we exploit this correspondence to obtain a classification of thec=9N=2 structures on solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or Kähler structures. 相似文献
4.
S. L. Woronowicz 《Communications in Mathematical Physics》1972,28(3):221-235
Let
be aC*-algebra and
be an opposite algebra. Notions of exact andj-positive states of
are introduced. It is shown, that any factor state of
can be extended to a pure exactj-positive state
of
. The correspondence
generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states 1 and 2 are quasi-equivalent if and only if their purifications
and
are equivalent. 相似文献
5.
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
6.
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
7.
Tomoyuki Arakawa Tomoki Nakanishi Kazuyuki Oshima Akihiro Tsuchiya 《Communications in Mathematical Physics》1996,181(1):157-182
We give thespectral decomposition of the path space of the
vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the
levell integrable modules, which is consistent with the earlier work [1] in the level one case. Also we prove the fermionic character formula of the
levell integrable representations in consequence. 相似文献
8.
Horng-Tzer Yau 《Communications in Mathematical Physics》1996,181(2):367-408
Let
denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let
be the corresponding canonical measure defined by conditioning
on
. Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed,
is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for
forall chemical potentials . We prove that
for any probability densityf with respect to
; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship. 相似文献
9.
We study analogues of the Yangian of the Lie algebra
for the other classical Lie algebras
and
. We call them twisted Yangians. They are coideal subalgebras in the Yangian of
and admit homomorphisms onto the universal enveloping algebras U(
) and U(
) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U(
) and U(
) of these subalgebras are also maximal commutative. 相似文献
10.
A quantum analogue of the dual pair
is introduced in terms of the oscillator representation of U
q
. Its commutant and the associated identity of Capelli type are discussed. 相似文献
11.
We show that the Ashtekar-Isham extension
of the configuration space of Yang-Mills theories
is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that
is contained in a zero measure subset of
with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on
. Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space
. 相似文献
12.
D. Arnaudon 《Czechoslovak Journal of Physics》1997,47(11):1075-1082
Irreducible representations of
at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra
not to be completely diagonalised. Some irreducible representations of
indeed contain indecomposable
-modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation. 相似文献
13.
Sergio Doplicher Daniel Kastler Derek W. Robinson 《Communications in Mathematical Physics》1966,3(1):1-28
Starting from aC*-algebra
and a locally compact groupT of automorphisms of
we construct a covariance algebra
with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations of
i.e. *-representations of
in which the automorphisms are continuously unitarily implemented. We further construct for relativistic field theory an algebra
yielding the *-representations of
in which the space time translations have their spectrum contained inV. The problem of denumerable occurence of superselection sectors is formulated as a condition on the spectrum of
. Finally we consider the covariance algebra
built with space translations alone and show its relevance for the discussion of equilibrium states in statistical mechanics, namely we restore in this framework the equivalence of uniqueness of the vacuum, irreducibility and a weak clustering property.On leave of absence from Istituto di Fisica G. Marconi — Roma. 相似文献
14.
Francesco Fidaleo 《Communications in Mathematical Physics》1986,107(2):233-240
Under the general assumptions of quantum field theory in terms of local algebras of field operators fulfilling the split property, we prove that any two local coveriant implementations of the gauge group (or, in the case of a connected and simply connected Lie gauge group, any two choices of local current algebras) relative to a pair of double cones
1,
2, are related by a unitary equivalence induced by a unitary in the algebra of observables localized in
2 which commutes with all fields localized in
1, where
1 is any double cone contained in the interior of
1, and
2 any double cone containing
2 in its interior. 相似文献
15.
Representations of theC*-algebra
of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of
onto its commutant. This means that there is an equivalent anti-linear representation of
in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed. 相似文献
16.
In the algebraic formulation the thermodynamic pressure, or free energy, of a spin system is a convex continuous functionP defined on a Banach space
of translationally invariant interactions. We prove that each tangent functional to the graph ofP defines a set of translationally invariant thermodynamic expectation values. More precisely each tangent functional defines a translationally invariant state over a suitably chosen algebra
of observables, i. e., an equilibrium state. Properties of the set of equilibrium states are analysed and it is shown that they form a dense set in the set of all invariant states over
. With suitable restrictions on the interactions, each equilibrium state is invariant under time-translations and satisfies the Kubo-Martin-Schwinger boundary condition. Finally we demonstrate that the mean entropy is invariant under time-translations. 相似文献
17.
Finitely generated free modular ortholattices. II 总被引:2,自引:0,他引:2
M. Haviar P. Konôpka C. B. Wegener 《International Journal of Theoretical Physics》1997,36(12):2661-2679
18.
We show that the action of the universalR-matrix of the affine
quantum algebra, whenq is a root of unity, can be renormalized by some scalar factor to give a well-defined nonsingular expression, satisfying the Yang-Baxter equation. It can be reduced to intertwining operators of representations, corresponding to Chiral Potts, if the parameters of these representations lie on the well-known algebraic curve.We also show that the affine
forq is a root of unity from the autoquasitriangular Hopf algebra in the sense of Reshetikhin.This work is supported by NATO linkage grant LG 9303057. 相似文献
19.
Let be a closed * derivation in aC* algebra
which commutes with an ergodic action of a compact group on
. Then generates aC* dynamics of
. Similar results are obtained for non-ergodic actions on abelianC* algebras and on the algebra of compact operators.Research supported by N.S.F. 相似文献
20.
Karl Kraus 《Communications in Mathematical Physics》1967,7(2):99-111
Concrete C*-algebras, interpreted physically as algebras of observables, are defined for quantum mechanics and local quantum field theory.Aquantum mechanical system is characterized formally by a continuous unitary representation up to a factorU
g
of a symmetry group
in Hilbert space and a von Neumann algebra on invariant with respect toU
g
. The set
of all operatorsX such thatU
g
X U
g
–1
, as a function ofg
, is continuous with respect to the uniform operator topology, is aC*-algebra called thealgebra of observables. The algebra is shown to be the weak (or strong) closure of
.Infield theory, a unitary representation up to a factorU(a, ) of the proper inhomogeneous Lorentz group
and local von Neumann algebras C for finite open space-time regionsC are assumed, with the usual transformation properties of
underU(a, ). The collection of allXC giving uniformly continuous functionsU (a, )X U
–1 (a, ) on
is then a localC*-algebra
, called thealgebra of local observables. The algebra
is again weakly (or strongly) dense in
c
. The norm-closed union
of the
for allC is calledalgebra of quasilocal observables (or quasilocal algebra).In either case, the group
is represented by automorphisms V
g
resp. V(a, ) — with V
g
X=U
g
X U
g
–1
— of theC*-algebra
, and this is astrongly continuous representation of
on the Banach space
. Conditions for V (a, ) can then be formulated which correspond to the usualspectrum condition forU (a, ) in field theory.Work supported in part by the Deutsche Forschungsgemeinschaft. 相似文献