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The quantum duality principle

Fabio Gavarini — 2002

Annales de l’institut Fourier

The “quantum duality principle” states that the quantization of a Lie bialgebra – via a quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more in detail, there exist functors 𝒬 𝒰 𝒜 𝒬 𝒮 𝒜 and 𝒬 𝒮 𝒜 𝒬 𝒰 𝒜 , inverse to...

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