548 research outputs found
Twisting adjoint module algebras
Transformation of operator algebras under Hopf algebra twist is studied. It
is shown that that adjoint module algebras are stable under the twist.
Applications to vector fields on non-commutative space-time are considered.Comment: 16 page
Deformation of orthosymplectic Lie superalgebra osp(1|2)
Triangular deformation of the orthosymplectic Lie superalgebra osp(1|4) is
defined by chains of twists. Corresponding classical r-matrix is obtained by a
contraction procedure from the trigonometric r-matrix. The carrier space of the
constant r-matrix is the Borel subalgebra.Comment: LaTeX, 8 page
Jordanian deformation of the open XXX-spin chain
The general solution to the reflection equation associated with the jordanian
deformation of the SL(2) invariant Yang R-matrix is found. The same K-matrix is
obtained by the special scaling limit of the XXZ-model with general boundary
conditions. The Hamiltonian with the boundary terms is explicitly derived
according to the Sklyanin formalism. We discuss the structure of the spectrum
of the deformed XXX-model and its dependence on the boundary conditions.Comment: 13 pages; typos correcte
Algebraic Bethe ansatz for the gl(12) generalized model II: the three gradings
The algebraic Bethe ansatz can be performed rather abstractly for whole
classes of models sharing the same -matrix, the only prerequisite being the
existence of an appropriate pseudo vacuum state. Here we perform the algebraic
Bethe ansatz for all models with , rational, gl(12)-invariant
-matrix and all three possibilities of choosing the grading. Our Bethe
ansatz solution applies, for instance, to the supersymmetric t-J model, the
supersymmetric model and a number of interesting impurity models. It may be
extended to obtain the quantum transfer matrix spectrum for this class of
models. The properties of a specific model enter the Bethe ansatz solution
(i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz
equations) through the three pseudo vacuum eigenvalues of the diagonal elements
of the monodromy matrix which in this context are called the parameters of the
model.Comment: paragraph added in section 3, reference added, version to appear in
J.Phys.
Three-magnon problem for exactly rung-dimerized spin ladders: from general outlook to Bethe Ansatze
Three-magnon problem for exactly rung-dimerized spin ladder is brought up
separately at all total spin sectors. At first a special duality transformation
of the equation is found within general outlook. Then
the problem is treated within Coordinate Bethe Ansatze. A straightforward
approach is developed to obtain pure scattering states. At values S=0 and S=3
of total spin the equation has the form inherent in the
chain. For solvability holds only in five previously found {\it
completely integrable} cases. Nevertheless a partial S=1 Bethe solution always
exists even for general non integrable model. Pure scattering states for all
total spin sectors are presented explicitly.Comment: 38 page
Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
There being no precise definition of the quantum integrability, the
separability of variables can serve as its practical substitute. For any
quantum integrable model generated by the Yangian Y[sl(3)] the canonical
coordinates and the conjugated operators are constructed which satisfy the
``quantum characteristic equation'' (quantum counterpart of the spectral
algebraic curve for the L operator). The coordinates constructed provide a
local separation of variables. The conditions are enlisted which are necessary
for the global separation of variables to take place.Comment: 15 page
Weyl approach to representation theory of reflection equation algebra
The present paper deals with the representation theory of the reflection
equation algebra, connected with a Hecke type R-matrix. Up to some reasonable
additional conditions the R-matrix is arbitrary (not necessary originated from
quantum groups). We suggest a universal method of constructing finite
dimensional irreducible non-commutative representations in the framework of the
Weyl approach well known in the representation theory of classical Lie groups
and algebras. With this method a series of irreducible modules is constructed
which are parametrized by Young diagrams. The spectrum of central elements
s(k)=Tr_q(L^k) is calculated in the single-row and single-column
representations. A rule for the decomposition of the tensor product of modules
into the direct sum of irreducible components is also suggested.Comment: LaTeX2e file, 27 pages, no figure
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