Contractions on the Classical Double

Details Contractions on the Classical Double Contractions on the Classical Double

1997-02-25

arxiv.org/abs/q-alg/9702031v1

Mathematics

Quantum Algebra

10 pages, LaTeX. M.O. contribution to Group 21, Goslar 1996

Scientific paper

Lie algebra contractions on the classical Drinfel'd Double of a given Lie bialgebra are introduced and compared to the usual Lie bialgebra contraction theory. The connection between both approaches turns out to be intimately linked to duality problems. The non-relativistic (Galilean) limit of a (1+1) Poincar\'e Double is used to illustrate the contraction process. Finally, it is shown that, in a certain sense, the classical limit in a quantum algebra can be thought as a certain contraction on the corresponding Double.

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