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1.
Two functionals and are introduced forC *-dynamical systems with invariant states and stationary channels. It is shown that the Kolmogorov-Sinai-type theorems hold for these functionals and . Our functionals and are set within the framework of quantum information theory and generalize a quantum KS entropy by CNT and the mutual entropy by Ohya.  相似文献   

2.
3.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups q(gl(2N+1)) is constructed as a twisting of the universal R-matrix S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's (N) q (gl(2N+1))), providing the factorization property of . As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo.  相似文献   

4.
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.
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   

6.
Let be a finite-dimensional complex simple Lie algebra and Uq( ) the associated quantum group (q is a nonzero complex number which we assume is transcendental). IfV is a finitedimensional irreducible representation of Uq( ), an affinization ofV is an irreducible representationVV of the quantum affine algebra Uq( ) which containsV with multiplicity one and is such that all other irreducible Uq( )-components ofV have highest weight strictly smaller than the highest weight ofV. There is a natural partial order on the set of Uq( ) classes of affinizations, and we look for the minimal one(s). In earlier papers, we showed that (i) if is of typeA, B, C, F orG, the minimal affinization is unique up to Uq( )-isomorphism; (ii) if is of typeD orE and is not orthogonal to the triple node of the Dynkin diagram of , there are either one or three minimal affinizations (depending on ). In this paper, we show, in contrast to the regular case, that if Uq( ) is of typeD 4 and is orthogonal to the triple node, the number of minimal affinizations has no upper bound independent of .As a by-product of our methods, we disprove a conjecture according to which, if is of typeA n,every affinization is isomorphic to a tensor product of representations of Uq( ) which are irreducible under Uq( ) (in an earlier paper, we proved this conjecture whenn=1).Both authors were partially supported by the NSF, DMS-9207701.  相似文献   

7.
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   

8.
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   

9.
The purpose of this Letter is to develop further the Gauss diagram approach to finite-type link invariants. In this context we introduce Gauss diagrams counterparts to chord diagrams, 4T relation, weight systems arising from Lie algebras, and an algebra of unitrivalent graphs modulo the STU relation. The counterparts, respectively, are arrow diagrams, 6T relation, weights arising from the solutions of the classical Yang–Baxter equation, and an algebra of acyclic arrow graphs (modulo an oriented version of the STU relation). The algebra encodes, in a graphical form, the main properties of Lie bialgebras, similarly to the well-known relation of the algebra of unitrivalent graphs to Lie algebras. We show that the oriented and relations hold, and that is isomorphic to the algebra of arrow diagrams. As an application, we consider an appropriate link-homotopy version of the algebra . Using this algebra, we construct a Gauss diagram invariants of string links up to link-homotopy, with values both in the algebra and in . We observe that this construction gives the universal Milnor's link-homotopy -invariants.  相似文献   

10.
For M a factor of type III1 we can find for every automorphism group s that commutes with a modular automorphism group t and another modular automorphism group , an automorphism group that commutes with is connected with s by an inner cocycle.  相似文献   

11.
We give a classification of the finite dimensional coadjoint orbits in the dual of the algebra + of polynomials in one variable with values in a semi-simple Lie algebra , and generalise this result to algebras defined over an arbitrary Riemann surface.During the preparation of this work the author was supported by NSERC grant A8361 and FCAR grant EQ3518.  相似文献   

12.
It was shown in an earlier paper that there is an Abelian extension of the general linear algebra gl 2, that contains the current algebra with anomaly in 3+1 dimensions. We construct a three-parameter family of deformations of . For certain choices of the deformation parameters, we can construct unitary representations. We also construct highest-weight nonunitary representations for all choices of the parameters.This work was supported in part by U.S. Department of Energy Contract No. DE-AC02-76ER13065.  相似文献   

13.
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   

14.
We prove a simple formula for the transverse Poisson structure to a coadjoint orbit (in the dual of a Lie algebra ) and use it in examples such as and . We also give a sufficient condition on the isotropy subalgebra of so that the transverse Poisson structureto the coadjoint orbit of is linear.  相似文献   

15.
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   

16.
Starting from conformal kinematics we show that the complex Minkowski space as a model of time-space is as good as the real one. A holomorphic field theory is constructed on and it is shown that real field theory is a linear approximation of the holomorphic one.  相似文献   

17.
By considering the cohomology of the loop algebraL , a representation ofL is constructed. the construction is based on a derivation ofL and a two-dimensional closed cochain ofl with coefficients in real numbersR 1. In the case of =0, the differential of the energy representation of the corresponding loop groupLG is derived.This work was supported in part by the National Natural Science Foundation of China.  相似文献   

18.
We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 107 producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).  相似文献   

19.
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted andZ 2-twisted theories, () and respectively, which may be constructed from a suitable even Euclidean lattice . Similarly, one may construct lattices and by analogous constructions from a doubly-even binary code . In the case when is self-dual, the corresponding lattices are also. Similarly, () and are self-dual if and only if is. We show that has a natural triality structure, which induces an isomorphism and also a triality structure on . For the Golay code, is the Leech lattice, and the triality on is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories () and with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.  相似文献   

20.
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   

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