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The garden of quantum spheres

Ludwik Dąbrowski (2003)

Banach Center Publications

A list of known quantum spheres of dimension one, two and three is presented.

The geometric reductivity of the quantum group S L q ( 2 )

Michał Kępa, Andrzej Tyc (2011)

Colloquium Mathematicae

We introduce the concept of geometrically reductive quantum group which is a generalization of the Mumford definition of geometrically reductive algebraic group. We prove that if G is a geometrically reductive quantum group and acts rationally on a commutative and finitely generated algebra A, then the algebra of invariants A G is finitely generated. We also prove that in characteristic 0 a quantum group G is geometrically reductive if and only if every rational G-module is semisimple, and that in...

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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