Contractions on the Classical Double

Angel Ballesteros; Mariano del Olmo

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arXiv · q-alg/9702031

Contractions on the Classical Double

Angel Ballesteros·Mariano del Olmo

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Abstract

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) Poincaré 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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Angel Ballesteros, Mariano del Olmo. 1997-02-25. Contractions on the Classical Double. https://arxiv.org/abs/q-alg/9702031

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