A.Yu. Alekseev, L.D. Faddeev, J. Frohlich, V. Schomerus. Representation theory of lattice current algebras. q-alg/9604017; Commun. Math. Phys. 191 (1998) 3160.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... chiral vertex operators (CVO) which are characterized essentially by the currents degrees of freedom with zero mode coefficients that are independent of the world sheet coordinate [15, 16, 13, 14] Such a type of quantum theory has been studied in the framework of lattice current algebras (see [8, 9, 10, 17, 18] and references therein) and has not been brought to a form yielding a satisfactory continuum limit . The direct investigation of the quantum model [13, 14, 1] has singled out a nontrivial gauge theory problem. This problem has been tackled in two steps [19, 20] in terms of a generalization of the ....

A.Yu. Alekseev, L.D. Faddeev, J. Frohlich, V. Schomerus. Representation theory of lattice current algebras. q-alg/9604017; Commun. Math. Phys. 191 (1998) 3160.

....correspond to their non interaction . Coxeter groups, braid groups, Hecke algebra etc. are examples of local groups and algebras. More generally, one can consider as z i not generators but subgroups or subalgebras. In the most recent time, such objects become popular in mathematical physics (see [12, 13]) Even more general notion is the localness with respect to a graph. In our case the graph is a chain. Another interesting case is a cycle, when generators are indexed with roots of unity. Definition 5. A locally free group LF k (semi group LF k , algebra) is a group (semi group, algebra ....

A. Alekseev, L. Faddeev, J. Frohlich, and V. Schmerus, Representation theory of lattice current algebras, Commun. Math. Phys. 191 (1998), 31.

....models of low dimensional quantum field theory during the last few years. Monodromy or loop algebras associated with quasitriangular Hopf algebras H play an important role in lattice approaches to Chern Simons theory [AGS] topological quantum field theory [AS] and current algebras on a circle [AFFS]. In these models they commonly appear as algebras generated by the matrix elements of quantum holonomy operators M = M I ab ) around closed loops. Their center is spanned by generators obeying the Verlinde algebra and commuting with all other link operators. Their represenation theory has been ....

....Supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik punctures. As a particular result the authors show that under the assumption on H to be a modular Hopf algebra the representation category of the associated monodromy algebra coincides with that of H itself [AS] In [AFFS] these results have been used and further developped to study current algebras on a periodic lattice chain. The authors introduce gauged loop algebras K given as crossed products of a monodromy algebra with a copy of the gauge quantum group sitting on the initial (j end) point of the loop. It ....

[Article contains additional citation context not shown here]

A.Yu. Alekseev, L.D. Faddev, J. Frohlich, V. Schomerus, Representation Theory of Lattice Current Algebras, q-alg/9604017.

....and P. Vecsernyes [SzV] have proposed an amplified version of the DHR theory, which also applies to locally finite dimensional lattice models. This setting has been further developed 1 see [BaWi] BL] G] DPR] FGV] FrKe] MS1,2] MoRe] Mu] PSa1] ReSm] Sz,V] 2 see [AFFS], AFSV] AFS] ByS] Fa] FG] KaS] NSz1,2] P] PSa2] SzV] by [NSz1,2] where based on the example of Hopf spin chains the authors proposed the notion of a universal localized cosymmetry ae : A A Omega G, incorporating all sectors ae I of A via ae I = id A Omega I ) ffi ae; ....

....G, incorporating all sectors ae I of A via ae I = id A Omega I ) ffi ae; I 2 Rep G. In the specific example studied by [NSz1,2] G was given by a quantum double and the cosymmetry ae was given by a coaction of G on A. Related results have later been obtained for lattice current algebras [AFFS], the later actually being a special case of the Hopf spin chains of [NSz1,2] see [N1] and Sect. 11.3) The analogue of a DHR field algebra for these models is now given by the standard crossed product F j A o G [NSz2] where G is the Hopf algebra dual to G. Now the methods and results of ....

[Article contains additional citation context not shown here]

A.Yu. Alekseev, L.D. Faddev, J. Frohlich, V. Schomerus, Representation Theory of Lattice Current Algebras, q-alg/9604017.

....model. A final step would involve performing the limit a 0 while keeping 6= 0. The realization of this program was started in [4, 5, 27] where a lattice regularization of the Kac Moody algebra has been proposed. Classical and quantum lattice current algebras were further investigated in [32, 6]. Our aim here is to extend the analysis of [6] by introducing chiral vertex operators. In comparison with the current algebra, the algebras of vertex operators contain (a finite number of) additional generators. Within these larger algebras we will be able to prepare a discrete analogue of the ....

....the limit a 0 while keeping 6= 0. The realization of this program was started in [4, 5, 27] where a lattice regularization of the Kac Moody algebra has been proposed. Classical and quantum lattice current algebras were further investigated in [32, 6] Our aim here is to extend the analysis of [6] by introducing chiral vertex operators. In comparison with the current algebra, the algebras of vertex operators contain (a finite number of) additional generators. Within these larger algebras we will be able to prepare a discrete analogue of the group valued field g(x) by combining left and ....

[Article contains additional citation context not shown here]

A.Yu.Alekseev, L.D.Faddeev, J.Frohlich, V.Schomerus, Representation theory of lattice current algebras, preprint q-alg/9604016 (1996).

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC