BRST Algebra Quantum Double and Quantization of the Proper Time Cotangent Bundle

The quantum double for the quantized BRST superalgebra is studied. The corresponding R-matrix is explicitly constucted. The Hopf algebras of the double form an analytical variety with coordinates described by the canonical deformation parameters. This provides the possibility to construct the nontrivial quantization of the proper time supergroup cotangent bundle. The group-like classical limit for this quantization corresponds to the generic super Lie bialgebra of the double.Comment: 11 pages, LaTe

Twists in U(sl(3)) and their quantizations

The solution of the Drinfeld equation corresponding to the full set of different carrier subalgebras in sl(3) are explicitly constructed. The obtained Hopf structures are studied. It is demonstrated that the presented twist deformations can be considered as limits of the corresponding quantum analogues (q-twists) defined for the q-quantized algebras.Comment: 31 pages, Latex 2e, to be published in Journ. Phys. A: Math. Ge

Quantization of Lie-Poisson structures by peripheric chains

The quantization properties of composite peripheric twists are studied. Peripheric chains of extended twists are constructed for U(sl(N)) in order to obtain composite twists with sufficiently large carrier subalgebras. It is proved that the peripheric chains can be enlarged with additional Reshetikhin and Jordanian factors. This provides the possibility to construct new solutions to Drinfeld equations and, thus, to quantize new sets of Lie-Poisson structures. When the Jordanian additional factors are used the carrier algebras of the enlarged peripheric chains are transformed into algebras of motion of the form G_{JB}^{P}={G}_{H}\vdash {G}_{P}. The factor algebra G_{H} is a direct sum of Borel and contracted Borel subalgebras of lower dimensions. The corresponding omega--form is a coboundary. The enlarged peripheric chains F_{JB}^{P} represent the twists that contain operators external with respect to the Lie-Poisson structure. The properties of new twists are illustrated by quantizing r-matrices for the algebras U(sl(3)), U(sl(4)) and U(sl(7)).Comment: 24 pages, LaTe