3 research outputs found
Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group
Braided groups and braided matrices are novel algebraic structures living in
braided or quasitensor categories. As such they are a generalization of
super-groups and super-matrices to the case of braid statistics. Here we
construct braided group versions of the standard quantum groups . They
have the same FRT generators but a matrix braided-coproduct \und\Delta
L=L\und\tens L where , and are self-dual. As an application, the
degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices
; it is a braided-commutative bialgebra in a braided category. As a
second application, we show that the quantum double D(\usl) (also known as
the `quantum Lorentz group') is the semidirect product as an algebra of two
copies of \usl, and also a semidirect product as a coalgebra if we use braid
statistics. We find various results of this type for the doubles of general
quantum groups and their semi-classical limits as doubles of the Lie algebras
of Poisson Lie groups.Comment: 45 pages. Revised (= much expanded introduction