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1.
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
2.
Theq=0 combinatorics for
is studied in connection with solvable lattice models. Crystal bases of highest weight representations of
are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq=0. It is shown that the crystal graphs for finite tensor products ofl-th symmetric tensor representations of
approximate the crystal graphs of levell representations of
. The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for
.Partially supported by NSF grant MDA904-90-H-4039 相似文献
3.
Richard V. Kadison 《Communications in Mathematical Physics》1982,85(1):143-154
Estimates for vector representations of states are used to prove that {C
n
C
0} is strong-operator convergent toC
0, whereC
n is the universal central support of
n
and {
n
} is a sequence of states of aC*-algebra
converging in norm to 0. States of
of a given type are shown to form a norm-closed convex subset of the (norm) dual of
. The pure states of
form a norm-closed subset of the dual.With partial support of the National Science Foundation (USA) 相似文献
4.
The theorem that each derivation of aC*-algebra
extends to an inner derivation of the weak-operator closure (
)– of
in each faithful representation of
is proved in sketch and used to study the automorphism group of
in its norm topology. It is proved that the connected component of the identity in this group contains the open ball of radius 2 with centerl and that each automorphism in extends to an inner automorphism of (
)–.Research conducted with the partial support of the NSF and ONR. 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.
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
7.
We characterize the finite-dimensional representations of the quantum affine algebra U
q
(
n+1) (whereq × is not a root of unity) which are irreducible as representations of U
q
(sl
n+1). We call such representations small. In 1986, Jimbo defined a family of homomorphismsev
a
from U
q
(sl
n+1) to (an enlargement of) U
q
(sl,n+1), depending on a parametera ·. A second family,ev
a
can be obtained by a small modification of Jimbo's formulas. We show that every small representation of U
q
(
n+1) is obtained by pulling back an irreducible representation of U
q
(sl
n+1) byev
a
orev
a
for somea ·. 相似文献
8.
We define a quantum-algebra associated to
as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary-algebra of
, or theq-deformed classical-algebra algebra of
. We construct free field realizations of the quantum-algebra and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in.The research of the second author was partially supported by NSF grant DMS-9501414. 相似文献
9.
We give a realization of the quantum affine Lie algebras
and
in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter q being related to the statistical parameter of the anyons by q = ei. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel [1] fermionic construction of undeformed affine Lie algebras. 相似文献
10.
The sequence of Jordan algebras
, whose elements are the 3×3 Hermitian matrices over the division algebras , , , and
, is considered. These algebras are naturally related to supersymmetric structures in space-time dimensions of 3, 4, 6, and 10, as the Lorentz groups in these dimensions can be expressed in a unified way as a subgroup of the structure group of the Jordan algebras
. The generators of the complete structure group and the automorphism group can be separated into bosonic and fermionic generators, depending on their transformation properties under the Lorentz subgroup. A peculiar connection between these fermionic generators and the supersymmetry generators of the superstring action is introduced and discussed. 相似文献
11.
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
12.
Using the Godement mean of positive-type functions over a groupG, we study -abelian systems {
, } of aC*-algebra
and a homomorphic mapping of a groupG into the homomorphism group of
. Consideration of the Godement mean off(g)U
g
withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) (
g
(A)) withA
and a covariant representation of the system {
, } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over
. Finally we investigate the discrete spectrum of covariant representations of {
, } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma. 相似文献
13.
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
14.
We construct affinization of the algebra
of complex size matrices, that contains the algebras
for integral values of the parameter. The Drinfeld-Sokolov Hamiltonian reduction of the algebra
results in the quadratic Gelfand-Dickey structure on the Poisson-Lie group of all pseudodifferential operators of complex order.This construction is extended to the simultaneous deformation of orthogonal and symplectic algebras which produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Partially supported by NSF grant DMS 9307086.Partially supported by NSF grant DMS 9401215. 相似文献
15.
Magnus B. Landstad 《Communications in Mathematical Physics》1977,52(2):191-202
One way of generalizing the definition of an action of the dual group of a locally compact abelian group on a von Neumann algebra to non-abelian groups is to consider (G)-comodules, where (G) is the Hopfvon Neumann algebra generated by the left regular representation ofG. To a (G)-comodule we shall associate a dual covariance algebra
and a natural covariant system (
, ,G), and in Theorem 1 the covariant systems coming from (G)-comodules are characterized. In [2] it was shown that the covariance algebra of a covariant system in a natural way is a (G)-comodule. Therefore one can form the dual covariance algebra of a covariance algebra and the covariance algebra of a dual covariance algebra. Theorems 2 and 3 deal with these algebras — generalizing a result by Takesaki. As an application we give a new proof of a theorem by Digernes stating that the commutant of a covariance algebra itself is a covariance algebra and prove the similar result for dual covariance algebras. 相似文献
16.
David Finkelstein Shlomit Ritz Finkelstein Christian Holm 《International Journal of Theoretical Physics》1986,25(4):441-463
Riemannian manifolds are but one of three ways to extrapolate from four-dimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors byN-ary hyperspinors with new internal components besides the usual two external ones, this leads to a second line, the hyperspin manifolds
and their tangent spaces
, different in structure and symmetry group from the Riemannian line, except that the binary spaces
(Minkowski time space) and
(Minkowskian manifold) lie on both.
and
have dimensionn=N
2. In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and theN-ary chronometric form is not quadratic, butN-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist. 相似文献
17.
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
18.
J. Donin 《Czechoslovak Journal of Physics》1997,47(11):1115-1122
For
we construct a two parametric
-invariant family of algebras,
, that is a quantization of the function algebra
on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric
-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on
. 相似文献
19.
S. Doplicher R. V. Kadison D. Kastler Derek W. Robinson 《Communications in Mathematical Physics》1967,6(2):101-120
We study pairs {
, } for which
is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of
. We examine, especially, those systems {
, } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A
g
(B) —
g
(B)A 0 asg for those states such that (
g
(A)) = (A) for allg inG andA in
). For concrete systems (those with
-acting on a Hilbert space andg
g
implemented by a unitary representationg U
g
on this space) we prove, among other results, that the operators commuting with
and {U
g
} form a commuting family when there is a vector cyclic under
and invariant under {U
g
}. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of {
,U
g
}. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics. 相似文献
20.
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