38 research outputs found
The Quantum Symplectic Cayley-Klein Groups
The contraction method applied to the construction of the nonsemisimple
quantum symplectic Cayley-Klein groups . This groups has been
realised as Hopf algebra of the noncommutative functions over the algebra with
nilpotent generators. The dual quantum algebras are constructed.Comment: 6 pages, LaTeX, submitted to Proceedings of ' II International
Workshop on Classical and Quantum Integrible Systems' (Dubna, 8-12
July,1996), to be published in Int.J.Mod.Phy
Contractions of Integrable Equations
The contraction is applied to obtaining of integrable systems associated with
nonsemisimple algebras. The effect of contraction is splitting off some
components from initial system without loss of integrability.Comment: 6 pages, LaTeX, submitted to Proceedings of ' II International
Workshop on Classical and Quantum Integrible Systems' (Dubna, 8-12
July,1996), to be published in Int.J.Mod.Phy
Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups
Quantum planes which correspond to all one parameter solutions of QYBE for
the two-dimensional case of GL-groups are summarized and their geometrical
interpretations are given. It is shown that the quantum dual plane is
associated with an exotic solution of QYBE and the well-known quantum -plane
may be regarded as the quantum analog of the flag (or fiber) plane.
Contractions of the quantum supergroup and corresponding quantum
superspace are considered in Cartesian basis. The contracted
quantum superspace is interpreted as the non-commutative
analog of the superspace with the fiber odd part.Comment: Talk given at the XIII Int. Coll. on Integrable Systems and Quantum
Groups, June 17-19, 2004, Prague, Czech Republic. Submitted in Czech. J. of
Physic