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

Superconformal Field Theory and SUSY N=1 KdV Hierarchy II: The Q-operator

The algebraic structures related with integrable structure of superconformal field theory (SCFT) are introduced. The SCFT counterparts of Baxter's Q-operator are constructed. The fusion-like relations for the transfer-matrices in different representations and their truncations are obtained.Comment: LaTeX2e, elsart.cls, 17 pages, Nuclear Physics B, 2005, in pres

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

Quantum group covariant systems

The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the transformation. Various algebras are considered which are covariant with respect to the quantum (super) groups $SU_q(2),\; SU_q(1, 1),\; SU_q(1|1),\; SU_q(n), \\ SU_q(m|n),\; OSp_q(1|2)$ as well as deformed Minkowski space-time algebras.Comment: 12 pages, Late

Reflection equations and q-Minkowski space algebras

We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties with respect the quantum Lorentz group action in a straightforward way.Comment: 10 page